`fmpz_bpoly_factor`

Synopsis#include <flint/fmpz_mpoly_factor.h>

void fmpz_bpoly_factor(fmpz_poly_t c, fmpz_tpoly_t F, fmpz_bpoly_t B)source

Factors the squarefree bivariate polynomial $B$ of positive degree in $x$ : sets $c$ to its content as a polynomial in $x$ over $\mathbb{Z}[y]$ and $F$ to the irreducible factors of the primitive part. The point $\alpha$ is the first of $0, 1, -1, 2, -2, \ldots$ for which $B(x, \alpha)$ keeps its degree and is squarefree; $B(x, \alpha)$ is factored with fmpz_poly_factor, the factors are lifted in $(\mathbb{Z}/p^k\mathbb{Z})[[y - \alpha]][x]$ to a precision given by a bound on the factors, and recombined by trying subsets. $B$ is destroyed. If $B$ is not squarefree, the search for $\alpha$ does not terminate.

Cite this page

The FLINT team, “fmpz_bpoly_factor (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_bpoly_factor.html (generated 2026-11-02).

@misc{flint-doc-fmpz-mpoly-factor-fmpz-bpoly-factor,
  author       = {{The FLINT team}},
  title        = {{fmpz\_bpoly\_factor (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_bpoly_factor.html},
  note         = {Generated 2026-11-02}
}

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