fmpz_bpoly_factor
#include <flint/fmpz_mpoly_factor.h>void fmpz_bpoly_factor(fmpz_poly_t c, fmpz_tpoly_t F, fmpz_bpoly_t B)sourceFactors 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.
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 2026-10-20).
@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 2026-10-20}
}