FLINT3.7.0-dev
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fq_nmod_mpoly_factor_irred_smprime_zassenhaus, fq_nmod_mpoly_factor_irred_smprime_wang, fq_nmod_mpoly_factor_irred_smprime_zippel, fq_nmod_mpoly_factor_irred_lgprime_zassenhaus, fq_nmod_mpoly_factor_irred_lgprime_wang, fq_nmod_mpoly_factor_irred_lgprime_zippel

Synopsis#include <flint/fq_nmod_mpoly_factor.h>
int fq_nmod_mpoly_factor_irred_smprime_zassenhaus(fq_nmod_mpolyv_t fac, const fq_nmod_mpoly_t A, const fq_nmod_mpoly_ctx_t ctx, flint_rand_t state)source
int fq_nmod_mpoly_factor_irred_smprime_wang(fq_nmod_mpolyv_t fac, const fq_nmod_mpoly_t A, const fq_nmod_mpoly_factor_t lcAfac, const fq_nmod_mpoly_t lcA, const fq_nmod_mpoly_ctx_t ctx, flint_rand_t state)source
int fq_nmod_mpoly_factor_irred_smprime_zippel(fq_nmod_mpolyv_t fac, const fq_nmod_mpoly_t A, const fq_nmod_mpoly_factor_t lcAfac, const fq_nmod_mpoly_t lcA, const fq_nmod_mpoly_ctx_t ctx, flint_rand_t state)source
int fq_nmod_mpoly_factor_irred_lgprime_zassenhaus(fq_nmod_mpolyv_t fac, const fq_nmod_mpoly_t A, const fq_nmod_mpoly_ctx_t ctx, flint_rand_t state)source
int fq_nmod_mpoly_factor_irred_lgprime_wang(fq_nmod_mpolyv_t Af, const fq_nmod_mpoly_t A, const fq_nmod_mpoly_factor_t lcAfac, const fq_nmod_mpoly_t lcA, const fq_nmod_mpoly_ctx_t ctx, flint_rand_t state)source
int fq_nmod_mpoly_factor_irred_lgprime_zippel(fq_nmod_mpolyv_t Af, const fq_nmod_mpoly_t A, const fq_nmod_mpoly_factor_t lcAfac, const fq_nmod_mpoly_t lcA, const fq_nmod_mpoly_ctx_t ctx, flint_rand_t state)source

Irreducible factorisation of a monic squarefree polynomial in at least three variables, given for the Wang and Zippel methods the factorisation lcAfac of the leading coefficient lcA in variable 0. The smprime versions use evaluation points in Fq\mathbb{F}_q; the lgprime versions map A into Fqn\mathbb{F}_{q^n} with the embeddings of fq_nmod_mpoly.h, factor there and multiply together the factors in each orbit of the Frobenius automorphism c↦cqc \mapsto c^q of Fqn\mathbb{F}_{q^n} over Fq\mathbb{F}_q. Return 1 for success, 0 if they ran out of evaluation points or extensions, and −1-1 for a failure that other points would not fix.

Cite this page

The FLINT team, “fq_nmod_mpoly_factor_irred_smprime_zassenhaus, fq_nmod_mpoly_factor_irred_smprime_wang, fq_nmod_mpoly_factor_irred_smprime_zippel, fq_nmod_mpoly_factor_irred_lgprime_zassenhaus, fq_nmod_mpoly_factor_irred_lgprime_wang, fq_nmod_mpoly_factor_irred_lgprime_zippel (fq_nmod_mpoly_factor.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/fq_nmod_mpoly_factor/fq_nmod_mpoly_factor_irred_smprime_zassenhaus.html (generated 2026-11-02).