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: info@maplesoft.on.ca
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 (128.97.4.254) and ftp.inria.fr (128.93.1.26).
Contact: questions about pari can be sent to pari@math.u-bordeaux.fr
and for the Macintosh versions to bernardi@mathp7.jussieu.fr
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: info-macsyma@macsyma.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
info@mathworks.com
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It has been superseded by a new and more powerful system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
magma@maths.su.oz.au
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: infodesk@nag.co.uk
Phone: +44 1865 311744
Fax: +44 1865 311755