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:1. Grobner basis: http://bollu.github.io/#computing-equivalent-gate-sets-using...2. Commutators of subgroups: http://bollu.github.io/#5age-code-to-play-around-with-commut...3. Graph/group theory: https://github.com/bollu/bollu.github.io/blob/2f88c28efc54fb...