Our favorite software for just about any computation is gp-pari. Although it’s primarily intended for computations in number theory, it’s very easy to use and supports lots of different areas of mathematics. Here are some resources to help you learn to use it, if you so choose.
Tutorials written by members of the PARI group.
A brief example session, showing some basic functionality.
The operators for admissible constructions we’ve developed in class.
A function to solve recursions, like for the various tree examples.
Some examples showing how these functions are used.