= sagemath

ff = GF(13)
ff(3)^(-1)   # the inverse element of 3 in a finite field with 13 elements is 9

R.<y> = PolynomialRing(GF(2), 'y')  # a binary polynomial ring
G = y^64+y^3+y^0                    # define a reduction polynomial
S.<x> = QuotientRing(R, R.ideal(G)) # define a quotient ring with the reduction polynomial
assert S.is_field()
S(x^1)^(-1)  # inverse element of x^1