`n_bpoly_mod_factor_smprime`

Synopsis#include <flint/nmod_mpoly_factor.h>

int n_bpoly_mod_factor_smprime(n_poly_t c, n_tpoly_t F, n_bpoly_t B, int allow_shift, nmod_t ctx)source

Factors the bivariate polynomial B in $x$ (main variable) and $y$ , which must be separable in $x$ : sets c to its content with respect to $x$ and F to its irreducible factors. Evaluates $y = \alpha$ for $\alpha \in \mathbb{F}_p$ (only $\alpha = 0$ if allow_shift is zero), factors the univariate image, lifts the factors $y$ -adically by Hensel lifting and recombines them with the linear algebra on logarithmic derivatives of Lecerf [Lec2006] (Bivariate factorisation). Returns 0 if no suitable $\alpha$ exists in $\mathbb{F}_p$ . B is destroyed.

References#

[Lec2006] G. Lecerf. Sharp precision in Hensel lifting for bivariate polynomial factorization. Mathematics of Computation 75 (2006), 921–933.

Cite this page

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

@misc{flint-doc-nmod-mpoly-factor-n-bpoly-mod-factor-smprime,
  author       = {{The FLINT team}},
  title        = {{n\_bpoly\_mod\_factor\_smprime (nmod\_mpoly\_factor.h)}},
  howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
  year         = {2026},
  url          = {https://flintlib.org/doc/nmod_mpoly_factor/n_bpoly_mod_factor_smprime.html},
  note         = {Generated 2026-11-02}
}

Edit this page · PDF version · Built with fdoc from 0a4634bf95