REDUCE is an interactive system for general algebraic computations of 
interest to mathematicians, scientists and engineers. It has been 
produced by a collaborative effort involving many contributors. Its 
capabilities include:

*  expansion and ordering of polynomials and rational functions;
*  substitutions and pattern matching in a wide variety of forms;
*  automatic and user controlled simplification of expressions;
*  calculations with symbolic matrices;
*  arbitrary precision integer and real arithmetic;
*  facilities for defining new functions and extending program syntax;
*  analytic differentiation and integration;
*  factorization of polynomials;
*  facilities for the solution of a variety of algebraic equations;
*  facilities for the output of expressions in a variety of formats;
*  facilities for generating optimized numerical programs from symbolic input;
*  calculations with a wide variety of special functions;
*  Dirac matrix calculations of interest to high energy physicists.

It is often used as an algebraic calculator for problems that are possible 
to do by hand. However,  REDUCE is designed to support calculations that 
are not feasible by hand.

WWW: http://www.reduce-algebra.com/