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?



Open source mathematical software
Here are some links.


* [Axiom](http://www.axiom-developer.org/) and [Maxima](http://maxima.sourceforge.net/) are good general purpose computer algebra systems.
* [DataMelt](http://jwork.org/dmelt/) is a free Java-based math software with a lot of examples
* [GAP](http://www.gap-system.org/) is a system for computational discrete algebra (with particular emphasis on computational group theory).
* [PARI/GP](http://pari.math.u-bordeaux.fr/) is a CAS for fast computations in number theory.
* [SAGE](http://www.sagemath.org/) is a kind of unified framework for several systems, including GAP, PARI, and Maxima.
* [Octave](http://www.gnu.org/software/octave/) is a system for numerical computations (it is close to Matlab).
* [Cadabra](http://cadabra.phi-sci.com/) is a computer algebra system designed for the solution of the field theory problems.
* [CoCoA](http://cocoa.dima.unige.it/) stands for "Computations in commutative algebra".
* [KANT / KASH](http://www.math.tu-berlin.de/~kant/kash.html) stands for "Computational Algebraic Number Theory".
* [Macaulay 2](http://www.math.uiuc.edu/Macaulay2/) is a system for research in commutative algebra and algebraic geometry.
* [Snap](http://snap-pari.sourceforge.net/) is a computer program for studying arithmetic invariants of hyperbolic 3-manifolds.
* [Symmetrica](http://www.algorithm.uni-bayreuth.de/en/research/SYMMETRICA/) is an object oriented computer algebra system for representations, combinatorics and applications of symmetric groups.


