I need a procedure to simplify rational functions r(x,y) = p(x,y)/q(x,y) where p(x,y) and q(x,y) are polynomials in Z/(2)[x,y].
For example suppose r(x,y) = (1+x+y)/(x^2+x*y+y+1) then mod 2 this reduces to 1/(1+x) since
Factor(x^2+x*y+y+1) mod 2 = (1 + x + y) (1 + x)
I wrote a procedure to do this using Factors mod 2, but I wonder if there is a builtin procedure to make such simplifications that might be more efficient. For now 2 variable is fine, but later I may want more than 2 variables.