This is not a comprehensive list. There are other Computer Algebra packages available that may better suit your needs. There is an Available Packages listing maintained at UC Berkeley. (The list can be obtained from math.berkeley.edu via anonymous ftp).
The <A HREF="http://symbolicnet.mcs.kent.edu/"> Symbolic Computation Network</a> contains lots of useful information.
A: Maple Purpose: Symbolic and numeric computation, mathematical programming, and mathematical visualization. Contact: Waterloo Maple Software, 450 Phillip Street Waterloo, Ontario N2L 5J2 Phone (519)747-2373 FAX (519)747-5284 email: firstname.lastname@example.org A: DOE-Macsyma Purpose: Symbolic and mathematical manipulations. Contact: National Energy Software Center Argonne National Laboratory 9700 South Cass Avenue Argonne, Illinois 60439 Phone: (708) 972-7250 A: Pari Purpose: Number-theoretic computations and simple numerical analysis. Available for most 32-bit machines, including 386+387 and 486. This is a copyrighted but free package, available by ftp from math.ucla.edu (22.214.171.124) and ftp.inria.fr (126.96.36.199). Contact: questions about pari can be sent to email@example.com and for the Macintosh versions to firstname.lastname@example.org A: Mathematica Purpose: Mathematical computation and visualization, symbolic programming. Contact: Wolfram Research, Inc. 100 Trade Center Drive Champaign, IL 61820-7237 Phone: 1-800-441-MATH A: Macsyma Purpose: Symbolic numerical and graphical mathematics. Contact: Macsyma Inc. 20 Academy Street Arlington, MA 02174 tel: 617-646-4550 fax: 617-646-3161 email: email@example.com A: Matlab Purpose: `matrix laboratory' for tasks involving matrices, graphics and general numerical computation. Contact: The MathWorks, Inc. 21 Prime Park Way Natick, MA 01760 508-653-1415 firstname.lastname@example.org A: Cayley/Magma A: Cayley/Magma Cayley is no longer being licenced or supported. It has been superseded by a new and more powerful system called Magma. Purpose: Computation in algebraic, geometric and combinatorial structures such as groups, rings, fields, algebras, modules, graphs and codes. Available for: SUN 3, SUN 4, SUN 10 (SUNOS 4.x and Solaris 2) DECstation (Ultrix), DEC Alpha (OSF/1), IBM RS6000 (AIX), HP9000/700 (HP-UX), Apollo M680x0, SGI, 486/Pentium (MS-DOS). Contact: Computational Algebra Group School of Mathematics and Statistics University of Sydney NSW 2006 Australia Phone: +61 2 351 3338 Fax: +61 2 351 4534 URL: http://www.maths.usyd.edu.au:8000/comp/magma/Overview.html email@example.com A: Axiom Purpose: Symbolic programming, symbolic and numeric computation, mathematical visualisation. Contact: The Numerical Algorithms Group Ltd Wilkinson House Jordan Hill Road Oxford OX2 8DR UK email: firstname.lastname@example.org Phone: +44 1865 311744 Fax: +44 1865 311755