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