gr_mpoly_divrem_ideal, gr_mpoly_divrem_ideal_heap_threaded, gr_mpoly_divrem_ideal_weak, gr_mpoly_divrem_ideal_weak_heap_threaded
#include <flint/gr_mpoly.h>int gr_mpoly_divrem_ideal(gr_mpoly_vec_t Q, gr_mpoly_t R, const gr_mpoly_t A, const gr_mpoly_vec_t B, gr_mpoly_ctx_t ctx)sourceint gr_mpoly_divrem_ideal_heap_threaded(gr_mpoly_vec_t Q, gr_mpoly_t R, const gr_mpoly_t A, const gr_mpoly_vec_t B, gr_mpoly_ctx_t ctx)sourceint gr_mpoly_divrem_ideal_weak(gr_mpoly_vec_t Q, gr_mpoly_t R, const gr_mpoly_t A, const gr_mpoly_vec_t B, gr_mpoly_ctx_t ctx)sourceint gr_mpoly_divrem_ideal_weak_heap_threaded(gr_mpoly_vec_t Q, gr_mpoly_t R, const gr_mpoly_t A, const gr_mpoly_vec_t B, gr_mpoly_ctx_t ctx)sourceDivision by a vector of divisors B_1, \ldots, B_k: A = \sum_i Q_i B_i + R, where no monomial of R is divisible by any leading monomial \operatorname{lm}(B_i) (the multivariate division algorithm, [CLO2015, §2.3]); the result depends on the order of the divisors unless they form a Gröbner basis. The weak versions accumulate inexact coefficient remainders as for gr_mpoly_divrem_weak. The output vector Q is resized to k entries.
Guides#
References#
- [CLO2015] D. Cox, J. Little and D. O'Shea. Ideals, Varieties, and Algorithms, fourth edition. Undergraduate Texts in Mathematics, Springer, 2015. https://doi.org/10.1007/978-3-319-16721-3
The FLINT team, “gr_mpoly_divrem_ideal, gr_mpoly_divrem_ideal_heap_threaded, gr_mpoly_divrem_ideal_weak, gr_mpoly_divrem_ideal_weak_heap_threaded (gr_mpoly.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/gr_mpoly/gr_mpoly_divrem_ideal.html (generated 2026-10-20).
@misc{flint-doc-gr-mpoly-gr-mpoly-divrem-ideal,
author = {{The FLINT team}},
title = {{gr\_mpoly\_divrem\_ideal, gr\_mpoly\_divrem\_ideal\_heap\_threaded, gr\_mpoly\_divrem\_ideal\_weak, gr\_mpoly\_divrem\_ideal\_weak\_heap\_threaded (gr\_mpoly.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/gr_mpoly/gr_mpoly_divrem_ideal.html},
note = {Generated 2026-10-20}
}