FLINT3.7.0-dev
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_fmpz_mod_poly_gcdinv, fmpz_mod_poly_gcdinv, _fmpz_mod_poly_gcdinv_euclidean, fmpz_mod_poly_gcdinv_euclidean

Synopsis#include <flint/fmpz_mod_poly.h>
slong _fmpz_mod_poly_gcdinv(fmpz * G, fmpz * S, const fmpz * A, slong lenA, const fmpz * B, slong lenB, const fmpz_mod_ctx_t ctx)source
void fmpz_mod_poly_gcdinv(fmpz_mod_poly_t G, fmpz_mod_poly_t S, const fmpz_mod_poly_t A, const fmpz_mod_poly_t B, const fmpz_mod_ctx_t ctx)source
slong _fmpz_mod_poly_gcdinv_euclidean(fmpz * G, fmpz * S, const fmpz * A, slong lenA, const fmpz * B, slong lenB, const fmpz_t invA, const fmpz_mod_ctx_t ctx)source
void fmpz_mod_poly_gcdinv_euclidean(fmpz_mod_poly_t G, fmpz_mod_poly_t S, const fmpz_mod_poly_t A, const fmpz_mod_poly_t B, const fmpz_mod_ctx_t ctx)source

Compute G=gcd⁡(A,B)G = \gcd(A, B) and SS, both reduced modulo BB, with G≡SA(modB)G \equiv SA \pmod B; when G=1G = 1, SS is the inverse of AA modulo BB. Requires len(B)≥2\mathit{len}(B) \ge 2 (an exception is raised otherwise); if A≡0(modB)A \equiv 0 \pmod B, sets G=S=0G = S = 0. The underscore versions require 0<lenA<lenB0 < \mathit{lenA} < \mathit{lenB}, write lenA coefficients of GG and lenB−1\mathit{lenB} - 1 of SS, and return the length of GG, which is not made monic. fmpz_mod_poly_gcdinv uses the Euclidean algorithm for lenB<16\mathit{lenB} < 16 and the extended half-GCD algorithm otherwise. The modulus must be prime.

Cite this page

The FLINT team, “_fmpz_mod_poly_gcdinv, fmpz_mod_poly_gcdinv, _fmpz_mod_poly_gcdinv_euclidean, fmpz_mod_poly_gcdinv_euclidean (fmpz_mod_poly.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/fmpz_mod_poly/_fmpz_mod_poly_gcdinv.html (generated 2026-11-02).