Mark Anderstam: Solution methods to polynomial equations over ℤ₂

We take a look at multivariable polynomial equations over Z_2 and describe the tools needed to find solutions in Z_2^n. We start by presenting a particular kind of solution method based on the fundamental "trial and error" strategy and we then use this to, eventually, find three different methods for solving these polynomial equations in a more systematic way. We later implement the solution methods in Python using arrays of booleans to represent monomials and asks which algorithm is more time efficient. We also say something about what could be improved in the future to make the algorithms more efficient and explain why further development of one algorithm is of greater interest to us.