Computer Algebra Software

SIGSAM maintains a collection of references to computer algebra systems and a consistent citation policy. Click the name of each system to see further information and linkes, including citation information.

General purpose commercial systems

Broad purpose free computer algebra systems

  • Axiom: a general-purpose, strongly typed, computer algebra system.
  • CoCoA: a computer algebra system for doing computations in Commutative Algebra.
  • Fermat: a computer algebra system oriented towards polynomial and matrix algebra over the rationals and finite fields.
  • GAP: a System for Computational Discrete Algebra.
  • KASH/KANT: computer algebra system for sophisticated computations in algebraic number fields and global function fields.
  • Macaulay2: a system for research in algebraic geometry and commutative algebra.
  • Reduce: an interactive system for general algebraic computations of interest to mathematicians, scientists and engineers.
  • SAGE: an open-source general purpose computer algebra system.
  • SINGULAR: a Computer Algebra System for polynomial computations with special emphasis on the needs of commutative algebra, algebraic geometry, and singularity theory.
  • PARI/GP: a computer algebra system designed for for fast computations in number theory.

Special Purpose Systems, Packages and Libraries

  • ACE : a Maple library providing tools useful in algebraic combinatorics.
  • Albert: an interactive program to assist the specialist in the study of nonassociative algebras.
  • ANUNQ: a GAP package for the computation of nilpotent factor groups of finitely presented groups.
  • ANUPQ: an interactive interface to the p-quotient, p-group generation and standard presentation algorithms of the ANU pq C program.
  • CALI: a REDUCE package for computational commutative algebra.
  • CASA: a Computer Algebra System for Algebraic Geometry.
  • CHEVIE: a computer algebra system for symbolic calculations with generic character tables of groups.
  • EinS: a Mathematica package allowing one to perform symbolic calculations with indexed objects.
  • Felix: a special computer algebra system for the computation in commutative and non-commutative rings and modules.
  • FeynArts: a Mathematica package for the generation and visualization of Feynman diagrams and amplitudes.
  • GiNaC: a system to allow the creation of integrated systems that embed symbolic manipulations together with more established areas of computer science.
  • GRAPE: a GAP package for constructing and analysing graphs related to groups, finite geometries, and designs.
  • GUAVA: a GAP package for computing with error-correcting codes.
  • LiDIA: A C++ Library For Computational Number Theory.
  • LiE: A Computer algebra package for Lie group computations.
  • MOLGEN: a system for the computation of all structural formulae that correspond to a given molecular formula.
  • ORME: a package for equational theoreies.
  • SONATA: a system for the construction and the analysis of finite nearrings.