`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)source

Sets $N$ 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#

Exact linear algebra over the integers

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 2026-11-02).

@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 2026-11-02}
}

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