fmpz_mat_solve_dixon
#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)sourceSolves 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.
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 2026-10-20).
@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 2026-10-20}
}