From: aicklen@utdallas.edu (Greg Aicklen)
Newsgroups: sci.math.symbolic
Subject: Inconsistent Mma results across platforms?
Date: 6 Nov 92 15:41:09 GMT
Article-I.D.: utdallas.1992Nov6.154109.6056
Organization: Univ. of Texas at Dallas

I am running the same version of Mma (2.1) on two different platforms and I
get different results in a symbolic operation.  Note that I am running the
Windows version of Mma 2.1, Student Edition on a 386SX with 10MB of RAM.

I seem to get different answers from ComplexExpand[] between the SPARC and
PC (windows) implementations of Mma 2.1.  Here is an example:

Mathematica 2.1 for SPARC
Copyright 1988-92 Wolfram Research, Inc.
 -- X11 windows graphics initialized --

In[1]:= eta = .

In[2]:= xbar = .

In[3]:= q[x_,t_] := 2 eta Sech[2 eta (x -xbar)] E^(4 I eta^2 t)

In[4]:= eta = 1;

In[5]:= xbar = 0;

In[6]:= qt[x_,t_] = D[q[x,t], t]

             4 I t
Out[6]= 8 I E      Sech[2 x]

In[7]:= qxx[x_,t_] = D[q[x,t], {x,2}]

            4 I t          3      4 I t                    2
Out[7]= -8 E      Sech[2 x]  + 8 E      Sech[2 x] Tanh[2 x]

In[8]:= fnls[x_,t_] = qt[x,t] - I qxx[x,t] - 2 I q[x,t]^2 Conjugate[q[x,t]]

             4 I t                  8 I t              4 I t
Out[8]= 8 I E      Sech[2 x] - 8 I E      Conjugate[2 E      Sech[2 x]]

               2          4 I t          3      4 I t                    2
>     Sech[2 x]  - I (-8 E      Sech[2 x]  + 8 E      Sech[2 x] Tanh[2 x] )

In[9]:= nls = fnls[x,t]

             4 I t                  8 I t              4 I t
Out[9]= 8 I E      Sech[2 x] - 8 I E      Conjugate[2 E      Sech[2 x]]

               2          4 I t          3      4 I t                    2
>     Sech[2 x]  - I (-8 E      Sech[2 x]  + 8 E      Sech[2 x] Tanh[2 x] )

In[10]:= nls = ComplexExpand[nls, TargetFunctions->{Re, Im}]

                      3
         -64 Cosh[2 x]  Sin[4 t]   16 Cosh[2 x] Sin[4 t]
Out[10]= ----------------------- - --------------------- +
                           3           1 + Cosh[4 x]
            (1 + Cosh[4 x])

                 2  -32 Cos[8 t] Cosh[2 x] Sin[4 t]
>    (4 Cosh[2 x]  (------------------------------- +
                             1 + Cosh[4 x]

          32 Cos[4 t] Cosh[2 x] Sin[8 t]                    2
>         ------------------------------)) / (1 + Cosh[4 x])  +
                  1 + Cosh[4 x]

                                    2
     16 Cosh[2 x] Sin[4 t] Sinh[4 x]
>    -------------------------------- +
                            3
             (1 + Cosh[4 x])

                             3
        64 Cos[4 t] Cosh[2 x]    16 Cos[4 t] Cosh[2 x]
>    I (---------------------- + --------------------- +
                          3          1 + Cosh[4 x]
           (1 + Cosh[4 x])

                    2  -32 Cos[4 t] Cos[8 t] Cosh[2 x]
>       (4 Cosh[2 x]  (------------------------------- -
                                1 + Cosh[4 x]

             32 Cosh[2 x] Sin[4 t] Sin[8 t]                    2
>            ------------------------------)) / (1 + Cosh[4 x])  -
                     1 + Cosh[4 x]

                                       2
        16 Cos[4 t] Cosh[2 x] Sinh[4 x]
>       --------------------------------)
                               3
                (1 + Cosh[4 x])

In[11]:= Simplify[nls]

Out[11]= 0

In[12]:=Quit

For the Windows version 2.1 (Student Version), the result of the ComplexExpand[] is

         3
Sech[2 x]  (8 (-2 + 2 Cos[8 t]) Sin[4 t] + 16 Cos[4 t] Sin[8 t]) +

            3
 I Sech[2 x]  (-8 Cos[4 t] (-2 + 2 Cos[8 t]) + 16 Sin[4 t] Sin[8 t])

and I (obviously) can't reduce this to zero.


Any ideas?  Anybody else able to duplicate this or seen something similar?

Greg Aicklen
aicklen@utdallas.edu
Newsgroups: sci.math.symbolic