I should have mentioned that more information about pysymbolic can be 
found at:

    http://cens.ioc.ee/projects/pysymbolic/design.html

This also has some interesting reference links (CAS=Computer Algebra 
System):

     NTL - a library for doing Number Theoryit contains very fast 
algorithm for factorization of polynomial; 
     GiNaC- "it does not try to provide extensive algebraic capabilities 
and a simple programming language but instead
     accepts a given language (C++) and extends it by a set of algebraic 
capabilities"; 
     CASs - quite excensive list of CASs; 
     Pari-GP- a software package for computer-aided number theory; 
     LiDIA- A C++ Library For Computational Number Theory; 
     YACAS- is an open source general purpose computer algebra system with 
a pleasant syntax; 
     CoCoA- is a special-purpose system for doing Computations in 
Commutative Algebra; 
     SIMATH- is a computer algebra system, especially for number theoretic 
purpose; 
     SACLIB- is a library of C programs for computer algebra; 
     Maxima- is a large computer algebra system for symbolic and numerical 
computations; 
     Macaulay 2- is a new software system devoted to supporting research 
in algebraic geometry and commutative algebra; 
     GAP- Groups, Algorithms and Programming. 
     General Purpose Computer Algebra Systems - an overview; 
     KANT/KASH- is a software package for mathematicians interested in 
algebraic number theory; 
     GROEBNER- is a system for computing Groebner bases, is free, is C 
library 

     Pythonica - a system for doing mathematics with Python; 
     Pysimplex- provides some basic symbolic programming tools for 
constructing, solving and optimizing systems of linear
     equations and inequalities. 

Conrad Schneiker
(This note is unofficial and subject to improvement without notice.)