`fmpz_mpolyl_gcd_hensel`

Synopsis#include <flint/fmpz_mpoly_factor.h>

int fmpz_mpolyl_gcd_hensel(fmpz_mpoly_t G, slong Gdeg, fmpz_mpoly_t Abar, fmpz_mpoly_t Bbar, const fmpz_mpoly_t A, const fmpz_mpoly_t B, const fmpz_mpoly_ctx_t ctx)

source

The EEZ-GCD algorithm [Wan1980] for $A$ and $B$ in at least two variables that are primitive as polynomials in $x_0$ , given an upper bound Gdeg on the degree in $x_0$ of the GCD: the variables $x_1, \ldots$ are evaluated at small integers, the univariate GCD is computed, and the factorisation $G \cdot \bar A$ of $A$ , of $B$ , or of a combination $\mu_1 A + \mu_2 B$ in which the two factors are coprime, is lifted with fmpz_mpoly_hlift.

References#

[Wan1980] P. S. Wang. The EEZ-GCD algorithm. ACM SIGSAM Bulletin 14:2 (1980), 50–60. https://doi.org/10.1145/1089220.1089228

Cite this page

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

@misc{flint-doc-fmpz-mpoly-factor-fmpz-mpolyl-gcd-hensel,
  author       = {{The FLINT team}},
  title        = {{fmpz\_mpolyl\_gcd\_hensel (fmpz\_mpoly\_factor.h)}},
  howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
  year         = {2026},
  url          = {https://flintlib.org/doc/fmpz_mpoly_factor/fmpz_mpolyl_gcd_hensel.html},
  note         = {Generated 2026-11-02}
}

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