GB and FGB  
   Software for solving algebraic equations: GB computes Groebner bases and FGB solves polynomial systems.
   http://www-calfor.lip6.fr/~jcf/

Macaulay 2  
   A new software system devoted to supporting research in algebraic geometry and commutative algebra.
   http://www.math.uiuc.edu/Macaulay2/

Computer Algebra and Problem Solving Environments  
   Abstract for Stanly Steinberg's article in "Comparative CAS Reviews and Philosophy", suggesting 6 ways in which computer algebra systems could be improved.
   http://math.unm.edu/~wester/aca96/Steinberg_abstract.html

Mathscribe  
   Mathscribe is free dynamic graphing and modeling software for use in algebra classes. Lesson plans for linears and quadratics are included.
   http://www.mathscribe.com/

Symmetrica  
   A collection of routines, written in C, for computing in the representation theory of classical and symmetric groups, and related areas. Public domain.
   http://www.mathe2.uni-bayreuth.de/axel/symneu_engl.html

CoCoA  
   A special-purpose system for computations in Commutative Algebra.
   http://cocoa.dima.unige.it/

Fermat  
   Computer algebra system that does arithmetic of arbitrarily long integers and fractions, symbolic calculations, graphics, and other numerical calculations. Free download. Documentation.
   http://www.bway.net/~lewis/

Comparison of Polynomial-Oriented Computer Algebra Systems  
   By Robert H. Lewis and Michael Wester. Presented as a poster to the 1999 ISSAC Conference.
   http://www.fordham.edu/lewis/cacomp.html

Algebra Problem Solver  
   Personal Algebra Tutor - Enter your algebra problems and get instant step-by-step solutions with explanations.
   http://www.cyberedinc.com/

GiNaC  
   An open framework for symbolic computation within the C++ programming language. The name GiNaC is an iterated and recursive abbreviation for "GiNaC is Not a CAS", where CAS stands for Computer Algebra System. Its design is revolutionary in a se
   http://www.ginac.de/

FRISCO - A Framework for Integrated Symbolic/Numeric Computation  
   The FRISCO project aims to develop highly efficient, versatile polynomial solvers for industrial users.
   http://www.nag.co.uk/projects/FRISCO.html

LAPACK -- Linear Algebra PACKage  
   written in Fortran77; provides routines for solving systems of simultaneous linear equations, least-squares solutions of linear systems of equations, eigenvalue problems, and singular value problems.
   http://netlib2.cs.utk.edu/lapack/

SymbolicNet  
   Directory of links on Symbolic Algebraic Computation: Frequently Asked Questions, Live Demos, software for download, events, bibliography, research groups, and researcher directory.
   http://www.SymbolicNet.org/

Aldor  
   Originally an extension to Axiom, now a separate product. Binaries are available free for non-profit use, with documentation, tips, projects and links.
   http://www.aldor.org/

Online Gröbner Basis Calculations  
   Online computation of reduced ideal bases.
   http://grobner.nuigalway.ie/

KAN  
   Rings and Computer algebra software, part of OpenXM.
   http://www.math.sci.kobe-u.ac.jp/KAN/

LAPACK++: Linear Algebra Package in C++  
   (v. 1.1a) a software library for numerical linear algebra; however, it does not include all of the capabilities of original f77 LAPACK.
   http://math.nist.gov/lapack++/

SINGULAR  
   Computer Algebra System for polynomial computations with special emphasis on commutative algebra, algebraic geometry, and singularity theory.
   http://www.singular.uni-kl.de/

Felix  
   Computer algebra system for computation in commutative and non-commutative rings and modules. Win32, Unix.
   http://felix.hgb-leipzig.de/

AXIOM  
   Symbolic solver complete with a high-level interactive language, user extensible library and visualisation tool for the manipulation of graphical output. For Unix and Windows. No longer produced: support ceases at the end of 2001.
   http://www.nag.co.uk/symbolic_software.asp

WinCoCoA Home Page  
   A version of CoCoA for Windows.
   http://www.physik.uni-regensburg.de/~krm03530/WinCoCoA.html

Combinatorial Representation Theory (CREP)  
   CREP is designed to deal with categories whose morphism spaces are finite-dimensional over a field k. The main example of a category with this property is the category of finite-dimensional representations of an associative unital k-algebra.
   http://www.mathematik.uni-bielefeld.de/~sek/crep.html

HartMath  
   An experimental computer algebra system written in Java and available free under GPL.
   http://www.hartmath.com/

MathPad - Scientific Matrices Calculator  
   Java applet based online Matrix calculation program for analyzing various simultaneous equations.
   http://www.mathpad.com/public/htmls/main/left/matrix/MatrixInfo.html

Computer Algebra Benchmarks  
   Collated by Computer Algebra Fachgruppe, Mannheim.
   http://krum.rz.uni-mannheim.de/cafgbench.html

Computer Algebra Pages and Servers  
   A collection of links.
   http://krum.rz.uni-mannheim.de/cabench/cawww.html

GIAC  
   Is A Computer algebra system. A semi-classical CAS by Bernard Parisse, available for Windows, Linux.
   http://www-fourier.ujf-grenoble.fr/~parisse/english.html

MAS - The Modula-2 Algebra System  
   MAS is an experimental computer algebra system with algebraic specification capabilities for the design and study of algebraic algorithms. Downloads, documentation.
   http://www.fmi.uni-passau.de/algebra/projects/mas.php3

JACAL  
   An interactive symbolic mathematics program. JACAL can manipulate and simplify equations, scalars, vectors, and matrices of single and multiple valued algebraic expressions containing numbers, variables, radicals, and algebraic differential, and holonomi
   http://swissnet.ai.mit.edu/~jaffer/JACAL.html

Math Forum - Algebra Software  
   Algebra software resources compiled by The Math Forum.
   http://mathforum.org/algebra/alg.software.html

Matrix Expression Templates (MET)  
   C++ matrix class library which promotes the notational convenience of linear algebraic codes. Free download.
   http://met.sourceforge.net/

GAP - Groups, Algorithms and Programming  
   A free system for computational discrete algebra.
   http://www-history.mcs.st-and.ac.uk/~gap/

Edu2000 Visual Algebra  
   Designed to ease the difficulties many students experience during the transition from arithmetic into the world of algebra using visualization. Covers linear and quadratic equations.
   http://www.mathematicssoftware.com/mathematics-software-html/algebra-1-software.php

Algebra Cheat  
   Program solves variable equations and gives explanations of steps used.
   http://www.bacsoftware.co.uk/algebra/

Schur  
   A package for Lie groups by Brian G. Wybourne. DOS, Win32, Unix. Ordering information.
   http://smc.vnet.net/Schur.html

Yet Another Computer Algebra System  
   A general purpose easy program for It is built on top of its own programming language designed for symbolic manipulation of math symbols. Includes information on how to use the software.
   http://yacas.sourceforge.net/

Math Symbolic Library  
   Evaluate, calculate, simplify and derive symbolic scalar, complex or vector expression. [OpenSource]
   http://www.cdrnet.net/projects/nmath/

Software for Computing Primitive Polynomials.  
   Free C software for computing primitive polynomials of degree n modulo p for p^n up to about 2^60.
   http://www.seanerikoconnor.freeservers.com/Mathematics/AbstractAlgebra/PrimitivePolynomials/overview.html

CMAT  
   A matrix calculator program, written in C. Calculations can be performed on matrices with complex rational coefficients using exact arithmetic routines, as well as on matrices with elements mod p.
   http://www.numbertheory.org/cmat/krm_cmat.html

Axiom Computer Algebra System  
   Savannah Free Software project for revival of Axiom as open source.
   http://savannah.nongnu.org/projects/axiom

gTybalt  
   An experimental free computer algebra system built on top of GiNaC, CLN and a program to interpret C and C++ commands.
   http://www.fis.unipr.it/~stefanw/gtybalt.html

Maxima  
   A GPL CAS based on DOE-MACSYMA. A GPL project.
   http://maxima.sourceforge.net/

perisic  
   A Java package for multivariate polynomials over polymorphic rings.
   http://ring.perisic.com/

LOWX  
   Parallel "low-index subgroups algorithm" software by Peter Dobcsányi for finding all subgroups up to given index in a finitely-presented group. Download documentation and binary distribution for Linux/i386 and Sparc/Solaris platforms.
   http://www.math.auckland.ac.nz/~peter/

FINITAS  
   Discussion group for this package for the construction and analysis of finite algebraic structures such as loops, quasigroups, and groups.
   http://groups.yahoo.com/group/finitas

Algebra Helper  
   Helps students with equations and inequalities, simplifying expression, graphing and complex numbers. Includes problem solving exercises.
   http://www.algebra-answer.com/

Galois Field Arithmetic Library  
   A simple opensource library in C++ for arithmetic between elements and polynomials over finite fields.
   http://www.partow.net/projects/galois/

A Tutorial Introduction To AXIOM  
   By Martin N. Dunstan.
   http://www.dcs.st-and.ac.uk/~mnd/documentation/axiom_tutorial/axiom.html

ZEN  
   A toolbox for computation in finite rings, by Florent Chabaud and Reynald Lercier. ANSI-C source, free download, GPL.
   http://fchabaud.free.fr/English/ZEN/

Algebra Word Problem Tutor:Miss Lindquist  
   The world's first web-delivered self-improving intelligent tutoring system able to tutor students in writing expressions for algebra word problems.
   http://www-2.cs.cmu.edu/~neil/

Macaulay  
   Macaulay is a computer algebra system for mathematical computations in algebraic geometry and commutative algebra. At its core is a carefully tuned implementation of Grobner basis methods for manipulating systems of polynomial equations.
   http://www.math.columbia.edu/~bayer/Macaulay/index.html

Albert  
   Albert is an interactive program to assist the specialist in the study of nonassociative algebra: the main problem addressed is the recognition of polynomial identities in varieties of nonassociative algebras. Download source code in C.
   http://www.cs.clemson.edu/~dpj/albertstuff/albert.html