`fmpz_mat_solve_dixon`

Synopsis#include <flint/fmpz_mat.h>

int fmpz_mat_solve_dixon(fmpz_mat_t X, fmpz_t mod, const fmpz_mat_t A, const fmpz_mat_t B)source

Solves $AX = B$ for a nonsingular square $A$ by $p$ -adic lifting and returns 1, or returns 0 if $A$ is singular. The solution is not reconstructed: $X$ is set to $A^{-1} B$ modulo mod, a power of a prime $p$ exceeding $2 \max(N, D)^2$ with $N$ and $D$ from fmpz_mat_solve_bound, with entries in $[0, \mathit{mod})$ , from which the rational entries can be reconstructed.

If $A$ or $B$ is empty, the function returns 1 without setting mod. Most applications should call fmpz_mat_solve_dixon_den, which reconstructs the solution (Several entries with a common denominator) and stops early when it is small.

Cite this page

The FLINT team, “fmpz_mat_solve_dixon (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_dixon.html (generated 2026-11-02).

@misc{flint-doc-fmpz-mat-fmpz-mat-solve-dixon,
  author       = {{The FLINT team}},
  title        = {{fmpz\_mat\_solve\_dixon (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_dixon.html},
  note         = {Generated 2026-11-02}
}

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