[Math] Open source mathematical software

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I want some recommendation on which software I should install on my computer. I'm looking for an open source program for general abstract mathematical purposes (as opposed to applied mathematics).

I would likely use it for group theory, number theory, algebraic geometry and probably polytopes.

The kind of program I have in mind is Mathematica or Matlab. Although probably those are not designed for abstract mathematics.

Any suggestions?

Best Answer

Here are some links.

  • Axiom and Maxima are good general purpose computer algebra systems.
  • DataMelt is a free Java-based math software with a lot of examples
  • 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 geometry.
  • 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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