REDUCE is a system for doing algebra by computer (CAS - Computer Algebra System), which also supports numerical approximation and interfaces to Gnuplot to provide graphics. REDUCE is implemented in standard Lisp expressed in an intuitive imperative-style notation called RLISP but this is completley hidden from the casual user. The latter is used as a basis for REDUCE's user-level language. The development of the REDUCE computer algebra system was started in the 1960s by Anthony C. Hearn. Since then, many scientists from all over the world have contributed to its development. REDUCE has a long and distinguished place in the history of computer algebra systems. Other systems that address some of the same issues but sometimes with rather different emphasis are Axiom, Maxima and so on. REDUCE is distributed for various architecture and/or operating system like GNU/Linux (Debian i686 and x86_64, Fedora Core i686 and x86_64, OpenSUSE i686 and x86_64, Scientific Linux i686, Ubuntu i686 and x86_64....), NetBSD i386, FreeBSD x86_64, PowerPC MAC Darwin and Solaris i386, and is complemented by numerous packages serving specialized mathematical purposes, which have to be loaded explicitly, e.g.;

For a list, but quite incomplete, click here. Its capabilities include:

• Expansion and ordering of polynomials and rational functions;
• Calculations with symbolic matrices;
• Arbitrary precision integer and real arithmetic;
• 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;
• Dirac matrix calculations of interest to high energy physicists.

Various REDUCE examples here.