This is already implemented in the sage i'm running (4.7.2.alpha2) sage: P.<x> = GF(2^10,'z')[] sage: p = P.random_element() sage: q = P.random_element() sage: p.inverse_mod(q) (z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z)*x + z^2 + z
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