In my case I literally mean the PolynomialReduce function in Wolfram Mathematica:  http://reference.wolfram.com/mathematica/ref/PolynomialReduce.html

So my TUInt32 class creates a symbolic representation of every mathematical or logical operator that is applied to it, and after each operation, it feeds that equation through Wolfram Mathematica to reduce and simplify the equation, for example: FullSimplify[PolynomialReduce[a*b, a0^2 - a0, b0^2 - b0, Modulus -> 2]]

(recall that logical operations are being transformed to numeric operations in the modulo 2 number ring)