_fmpz_mat_certify_singular_lu_mod_p
Synopsis
#include <flint/fmpz_mat.h>int _fmpz_mat_certify_singular_lu_mod_p(const fmpz_mat_t A, slong rank, const slong * P, const slong * pivs, ulong p)sourceGiven the rank r < n of the m \times n matrix A modulo the prime p and its echelon structure (P and pivs as from nmod_mat_lu_with_pivots), tries to prove that A has rank less than n by exhibiting a nonzero integer kernel vector, obtained by solving the pivot block against the first non-pivot column. Returns 1 if this succeeds and 0 otherwise; a return value of 1 is a proof whatever p.
Cite this page
The FLINT team, “_fmpz_mat_certify_singular_lu_mod_p (fmpz_mat.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/fmpz_mat/_fmpz_mat_certify_singular_lu_mod_p.html (generated 2026-10-20).
@misc{flint-doc-fmpz-mat-fmpz-mat-certify-singular-lu-mod-p,
author = {{The FLINT team}},
title = {{\_fmpz\_mat\_certify\_singular\_lu\_mod\_p (fmpz\_mat.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/fmpz_mat/_fmpz_mat_certify_singular_lu_mod_p.html},
note = {Generated 2026-10-20}
}