How to divide two polynomials in GF(2)[x] and get result in same type as of operands [closed]

edit

Like this:

sage: R.<x> = PolynomialRing(GF(2))
sage: f = x^3 - 1
sage: g = x - 1
sage: f // g
x^2 + x + 1
sage: type(f // g)
<class 'sage.rings.polynomial.polynomial_gf2x.Polynomial_GF2X'>
sage: (f // g).parent() is R
True

Or if you have an element of the fraction field which equals a fraction with a unit in the denominator, you can convert it into an element of R:

sage: R(f / g)
x^2 + x + 1