fmpz_mat_charpoly_bound
Synopsis
#include <flint/fmpz_mat.h>void fmpz_mat_charpoly_bound(fmpz_t bound, const fmpz_mat_t A)sourceSets bound to an upper bound for the absolute values of the coefficients of the characteristic polynomial of the square matrix .
The coefficient of is the sum of the principal minors. By Hadamard's inequality each minor is at most the product of the largest row norms of , and also of the largest column norms. The function returns the smaller of the maxima over of times these products.
Guides#
Cite this page
The FLINT team, “fmpz_mat_charpoly_bound (fmpz_mat.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/fmpz_mat/fmpz_mat_charpoly_bound.html (generated 2026-11-02).
@misc{flint-doc-fmpz-mat-fmpz-mat-charpoly-bound,
author = {{The FLINT team}},
title = {{fmpz\_mat\_charpoly\_bound (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_charpoly_bound.html},
note = {Generated 2026-11-02}
}