FLINT3.7.0-dev
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acb_mat_det_lu, acb_mat_det_precond, acb_mat_det

Synopsis#include <flint/acb_mat.h>
void acb_mat_det_lu(acb_t det, const acb_mat_t A, slong prec)source
void acb_mat_det_precond(acb_t det, const acb_mat_t A, slong prec)source
void acb_mat_det(acb_t det, const acb_mat_t A, slong prec)source

Set det to an enclosure of the determinant of the square matrix AA. The lu version uses Gaussian elimination and bounds the remaining submatrix by Hadamard's inequality when no more pivots can be found; the precond version multiplies AA by approximate inverses of the factors of an approximate LU decomposition and encloses the determinant of the result, which is close to the identity [Rum2010]. The default uses direct formulas for n≤3n \le 3 and triangular matrices, the lu version if n≤14n \le 14 or prec>10n\mathit{prec} > 10n, and the precond version otherwise; it throws an exception for a non-square matrix.

References#

  • [Rum2010] S. M. Rump, "Verification methods: Rigorous results using floating-point arithmetic", Acta Numerica 19 (2010), 287-449.
Cite this page

The FLINT team, “acb_mat_det_lu, acb_mat_det_precond, acb_mat_det (acb_mat.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_mat/acb_mat_det_lu.html (generated 2026-11-02).