Computer Algebra Links

SymbolicNet (Symbolic Mathematical Computation Information Center)

Combinatorial Software and Databases
(Séminaire Lotharingien de Combinatoire)

Mathematica (Wolfram Research).

Maple (Waterloo Maple)

Reduce
(an interactive program designed for general algebraic computations of
interest to mathematicians, scientists and engineers)

Matlab (integrates mathematical computing, visualization, and a
powerful language to provide a flexible environment for technical computing)

Octave (GNU Octave is a highlevel language, primarily intended for
numerical computations. It is mostly compatible with Matlab.)

Sage
(a free opensource mathematics software system)

Mathemagix
(a free computer algebra system under development)

GAP

Magma

Macaulay2

SINGULAR
(for polynomial computations)

ACE (Algebraic Combinatorics Environment)

LiE (Lie theory computations)

Home Page for SF (Symmetric Functions), posets, and coxeter/weyl
(John Stembridge's Maple packages)

MOPS, Multivariate orthogonal polynomials (symbolically)

Felix
(for computation in commutative and noncommutative rings and modules)

computer algebra and special functions (Tom Koornwinder)

Schubert,
a Maple package for intersection theory and enumerative geometry
(Sheldon Katz, Stein Arild Strømme, JanMagnus Økland)

FeynCalc, Tools and Tables for Quantum Field Theory Calculations
(in Mathematica).

Hyperdire,
a set of Mathematica based programs for differential reduction
of Horn type hypergeometrical functions.

AXIOM

NCAlgebra (noncommutative algebra package in Mathematica)

CLIFFORD (a Maple package for Clifford algebra computations)

FORM (program for large scale symbolic manipulation)
by Jos Vermaseren.

RATE  A Mathematica guessing machine
(by Christian Krattenthaler:
to guess a closed form expression for a sequence of numbers
or rational functions

Algolib:
combinatorics package for Maple by Bruno Salvy and coworkers (INRIA, France)

Haskell
(a purely functional programming language)

GrInvIn,
an interactive software application for studying graphs and their invariants

pages on fast algorithms by Ekatherina Karatsuba:

Documentation on the Gröbner Package for Gap 4
by A.M. Cohen and D.A.H. Gijsbers (TU Eindhoven)

Perfectly Scientific, Inc. (PSI), an algorithm company.
They offer
PrimeKit: Mathematica implementations for the algorithms in the book
R. Crandall and C. Pomerance,
Prime numbers.

Schoonschip was instrumental in the research by Martinis Veltman leading to
his
Nobel Prize in Physics 1999.
to Tom Koornwinder's home page