I suggest using Maxima, which has strong connection to Tcl and also has Tcl/Tk GUI frontend.

See information about Maxima and its usage from Tcl at http://mini.net/tcl/4758

you could feed maxima.exe with your data and read results
This involves 2-way pipes

Another approach could be to start Tcl/Tk GUI for maxima and manipulate this GUI from Perl to get your results.

addition 1,2:

I get my 2nd way to work, but this required some Tcl touches and looking Tcl/Tk wiki for some Maxima connection details.
But finally I got Perl+Tcl/Tk gui with a button that do symbolic algebra computations 

use strict;
use Tcl;
use Tcl::Tk;

my $int = new Tcl::Tk; # this one for Maxima GUI
my $int2 = new Tcl::Tk;
my $mwm = $int->mainwindow;
my $mw = $int2->mainwindow;

# get maxima
$int->Eval('source xmaxima0');
$int->Eval('source m0.tcl');

# do our GUI

my $text_res;
my $str = 'integrate(1/(1+x^3),x)'; # text example for maxima expr

$mw->Entry(-font=>'Courier 12',-textvariable=>\$str)->pack(-fill=>'x')
+;
$mw->Button(-text=>'Do it!',-command=>sub {
  $text_res->insert('end',''.$int->domax($str));
  $text_res->seeEnd;
})->pack;
$text_res = $mw->Scrolled('Text',-font=>'Courier 12')->pack;

$mwm->withdraw;

$int2->MainLoop;
$mwm->destroy;

[download]
Happy screenshot at http://www.vkonovalov.ru/xmaxima-scr.jpg

In reply to Re: Perl and maths by Courage
in thread Perl and maths by ReinhardE

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.