`fq_mat_lu`

Synopsis#include <flint/fq_mat.h>

slong fq_mat_lu(slong * P, fq_mat_t A, int rank_check, const fq_ctx_t ctx)

Computes a generalised LU decomposition $PA = LU$ of $A$ in place, and returns the rank of $A$ . P must have room for as many entries as $A$ has rows; it receives the row permutation.

If $A$ is a nonsingular square matrix, it is overwritten with the unit lower triangular $L$ (without its diagonal) and the upper triangular $U$ . If $A$ has rank $r$ , then $U$ is in row echelon form with $r$ nonzero rows, and $L$ is lower triangular with $r$ columns and implicit ones on its diagonal. If rank_check is nonzero and $A$ is found to be rank-deficient, the function stops early and returns 0, leaving $A$ in an undefined state.

Cite this page

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

@misc{flint-doc-fq-mat-fq-mat-lu,
  author       = {{The FLINT team}},
  title        = {{fq\_mat\_lu (fq\_mat.h)}},
  howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
  year         = {2026},
  url          = {https://flintlib.org/doc/fq_mat/fq_mat_lu.html},
  note         = {Generated 2026-11-02}
}

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