List of free mathematical software
The list below presents an absolutely arbitrary selection of software I know about that can be used for mathematical (mostly algebraic) computation. There are a lot of omissions since either I don't know about some apps or I don't consider them worth mentioning. As mentioned above, the selection is purely arbitrary, so please don't mail me about a java-based calculator you have happened to write that you wish to be included. I won't. Period.
General purpose
- Maxima — easy to use, good GUI, no support for finite fields;
- Reduce — not so good GUI as Maxima, finite fields partially supported, some rough edges;
- Axiom — very powerful, as user friendly as a pit-bull with headache;
- Sage — in theory it combines various other tools, huge;
Commutative algebra and algebraic geometry
Group theory
- GAP — the standard tool for computational group theory;
- Magnus — works with infinite groups, strange UI;
Number theory
Numerical methods and statistics
- SciLab — my preferred;
- Octave — free Matlab clone;
- R — free S clone;