fmpz_mpolyl_gcd_zippel2
#include <flint/fmpz_mpoly_factor.h>int fmpz_mpolyl_gcd_zippel2(fmpz_mpoly_t G, fmpz_mpoly_t Abar, fmpz_mpoly_t Bbar, const fmpz_mpoly_t A, const fmpz_mpoly_t B, const fmpz_mpoly_t Gamma, const fmpz_mpoly_ctx_t ctx)sourceThe sparse GCD of Hu and Monagan [HuMon2016] for A and B in at least three variables that are primitive as polynomials in x_0, x_1 over \mathbb{Z}[x_2, \ldots, x_{n-1}]: bivariate GCDs in x_0, x_1 modulo primes, with the remaining variables evaluated at powers of random points, are interpolated with the Berlekamp–Massey algorithm, and the result is verified by division. Gamma, a polynomial in x_2, \ldots that is a multiple of the leading coefficient of the GCD in x_0, x_1 (in practice the GCD of the leading coefficients of A and B), is imposed on the images.
References#
- [HuMon2016] J. Hu and M. Monagan. A fast parallel sparse polynomial GCD algorithm. Proceedings of ISSAC 2016, ACM, 271–278; full version in Journal of Symbolic Computation 105 (2021), 28–63. https://doi.org/10.1016/j.jsc.2020.06.001
The FLINT team, “fmpz_mpolyl_gcd_zippel2 (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_zippel2.html (generated 2026-10-20).
@misc{flint-doc-fmpz-mpoly-factor-fmpz-mpolyl-gcd-zippel2,
author = {{The FLINT team}},
title = {{fmpz\_mpolyl\_gcd\_zippel2 (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_zippel2.html},
note = {Generated 2026-10-20}
}