fmpz_mat_det_bound, fmpz_mat_det_bound_submatrix
Synopsis
#include <flint/fmpz_mat.h>void fmpz_mat_det_bound(fmpz_t bound, const fmpz_mat_t A)sourcevoid fmpz_mat_det_bound_submatrix(fmpz_t bound, const fmpz_mat_t A)sourceSets bound to an upper bound for |\det(A)|: the smaller of the products of the Euclidean norms of the rows and of the columns (Hadamard's inequality [Had1893]), rounded up. The submatrix variant omits zero rows and columns from the products, which yields a bound for the absolute value of every minor of A (of any size), also for nonsquare A. The bound of an empty matrix is 1.
Guides#
References#
- [Had1893] J. Hadamard. Résolution d'une question relative aux déterminants. Bulletin des Sciences Mathématiques 17 (1893), 240–246.
Cite this page
The FLINT team, “fmpz_mat_det_bound, fmpz_mat_det_bound_submatrix (fmpz_mat.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/fmpz_mat/fmpz_mat_det_bound.html (generated 2026-10-20).
@misc{flint-doc-fmpz-mat-fmpz-mat-det-bound,
author = {{The FLINT team}},
title = {{fmpz\_mat\_det\_bound, fmpz\_mat\_det\_bound\_submatrix (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_det_bound.html},
note = {Generated 2026-10-20}
}