FLINT3.7.0-dev
/

_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) and S, both reduced modulo B, with G \equiv SA \pmod B; when G = 1, S is the inverse of A modulo B. Requires \mathit{len}(B) \ge 2 (an exception is raised otherwise); if A \equiv 0 \pmod B, sets G = S = 0. The underscore versions require 0 < \mathit{lenA} < \mathit{lenB}, write lenA coefficients of G and \mathit{lenB} - 1 of S, and return the length of G, which is not made monic. fmpz_mod_poly_gcdinv uses the Euclidean algorithm for \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 2026-10-20).