fmpz_mat_solve_bound
Synopsis
#include <flint/fmpz_mat.h>void fmpz_mat_solve_bound(fmpz_t N, fmpz_t D, const fmpz_mat_t A, const fmpz_mat_t B)sourceSets N and D to bounds for the solution of AX = B written over the denominator \det(A): D \ge |\det(A)| and N \ge the absolute value of every entry of \det(A) A^{-1} B.
D is the smaller of the row and column Hadamard bounds. N is the product of the column norms of A with one factor replaced by the largest column norm of B, by Cramer's rule and Hadamard's inequality applied to columns; the row bound cannot be used for N. All norms are accumulated with upward rounding in mag_t arithmetic.
Guides#
Cite this page
The FLINT team, “fmpz_mat_solve_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_solve_bound.html (generated 2026-10-20).
@misc{flint-doc-fmpz-mat-fmpz-mat-solve-bound,
author = {{The FLINT team}},
title = {{fmpz\_mat\_solve\_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_solve_bound.html},
note = {Generated 2026-10-20}
}