Is there any package in python or java that can solve a system of linear equations over a finite field? I'm trying to solve 20+ equations with 20+ unknown variables and having this package would be great. This is a system of equations over a finite field so it's not quite the same as solving regular linear equations.
Additions, subtraction, multiplication, and division follow the set of rules described here for finite fields. Thanks.
Try Sage.
It's very powerful mathematics system written in Python. It's syntax is nearly identical as Python's.
Finite field operations are in this package.