Free CA Software

Aldor   (the Axiom Library Compiler) - integrating Computer Algebra and Reasoning.

Axiom - a general purpose Computer Algebra system.

Cadabra   is a new computer algebra system designed specifically for the solution of problems encountered in field theory. It has extensive functionality for tensor polynomial simplification taking care of Bianchi and Schouten identities, for fermions and anti-commuting variables, Clifford algebras and Fierz transformations, implicit coordinate dependence, multiple index types and many other field theory related concepts. The input format is a subset of TeX and thus easy to learn. Both a command-line and a graphical interface are available.

Here is the Introducing Cadabra by K. Peeters.

Calc 3D - an international freeware program for calculating 3-dimensional vectors, matrices, complex numbers and quaternions with Windows 98/NT.

CoCoA  is a freely available system for computing with multivariate polynomials. CoCoA deals with computations in multivariate polynomial rings over the rationals or modular integers, and on their ideals and modules. The implementation of the ideal/module theoretic operations relies on Grobner basis theory.

Fermat  -  a Computer Algebra system for Polynomial and Matrix Computation.

FORM - a program for large scale symbolic manipulation.

GAP - Groups, Algorithms and Programming. GAP is a free system for computational discrete algebra.

KANT - a Computer Algebra system for sophisticated computations in algebraic number fields.

Macaulay 2   This system supports research in algebraic geometry and commutative algebra.

Maxima - a system for the manipulation of symbolic and numerical expressions.

MOLGEN, Bayreuth University. This program system is devoted to generating all structures that correspond to a given molecular formula.

Mu PAD ® Pro is an open mathematical problem solving environment, also known as computer algebra system (CAS), for exact symbolic and numeric computing with arbitrary precision.

NZMATH  is a Python based number theory oriented calculation system. It is developed at Tokyo Metropolitan University. It is freely available and distributed under the BSD license.
NZMATH is new SIMATH.

REDUCE    is now available free of charge from SourceForge .

Risa/Asir   is an open source general computer algebra system.

Singular - a Computer Algebra System for Polynomial Computations.

SYMMETRICA , Bayreuth University.

Yacas - a general purpose Computer Algebra System.

Derive - a powerful system for doing symbolic and numeric mathematics on the PC.

Magma - the Computer Algebra System for Algebra, Number Theory and Geometry.