Open source mathematical software
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.
GAP is fantastic for group theory, combinatorics and and number theory. Sage is becoming very popular and essentially includes GAP as well.
Oberwolfach recently started a site listing mathematical software, sorted by subject: Oberwolfach References on Mathematical Software.