SageMath – Open-Source Mathematical Software System
I'm a huge fan of SAGE! I keep using it to discover new math. I generally play with the associate Sage module of any algebraic structure to get a real feel for what is going on. Some examples of:<p>1. Grobner basis: <a href="http://bollu.github.io/#computing-equivalent-gate-sets-using-grobner-bases" rel="nofollow">http://bollu.github.io/#computing-equivalent-gate-sets-using...</a><p>2. Commutators of subgroups: <a href="http://bollu.github.io/#5age-code-to-play-around-with-commutators-of-" rel="nofollow">http://bollu.github.io/#5age-code-to-play-around-with-commut...</a><p>3. Graph/group theory: <a href="https://github.com/bollu/bollu.github.io/blob/2f88c28efc54fb16463e2d9e0ac63f28620e223b/content/blog/math/intro_to_sage.md" rel="nofollow">https://github.com/bollu/bollu.github.io/blob/2f88c28efc54fb...</a>