Post Made Community Wiki by S. Carnahan
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Here are some links.

  • Axiom and Maxima are good general purpose computer algebra systems.
  • GAP is a system for computational discrete algebra (with particular emphasis on computational group theory).
  • PARI/GP is a CAS for fast computations in number theory.
  • SAGE is a kind of unified framework for several systems, including GAP, PARI, and Maxima.
  • Octave is a system for numerical computations (it is close to Matlab).
  • Cadabra is a computer algebra system designed for the solution of the field theory problems.
  • CoCoA stands for "Computations in commutative algebra".
  • KANT / KASH stands for "Computational Algebraic Number Theory".
  • Macaulay 2 is a system for research in commutative algebra and algebraic geometryresearch.
  • Snap is a computer program for studying arithmetic invariants of hyperbolic 3-manifolds.
  • Symmetrica is an object oriented computer algebra system for representations, combinatorics and applications of symmetric groups.
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Here are some links.

  • Axiom and Maxima are good general purpose computer algebra systems.
  • GAP is a system for computational discrete algebra (with particular emphasis on computational group theory).
  • PARI/GP is a CAS for fast computations in number theory.
  • SAGE is a kind of unified framework for several systems, including GAP, PARI, and Maxima.
  • Octave is a system for numerical computations (it is close to Matlab).
  • Cadabra is a computer algebra system designed for the solution of the field theory problems.
  • CoCoA stays stands for "Computations in commutative algebra".
  • KANT / KASH stands for "Computational Algebraic Number Theory".
  • Macaulay 2 is a system for algebraic geometry research.
  • Snap is a computer program for studying arithmetic invariants of hyperbolic 3-manifolds.
  • Symmetrica is an object oriented computer algebra system for representations, combinatorics and applications of symmetric groups.
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