fmpz_mat_rank
Synopsis
#include <flint/fmpz_mat.h>slong fmpz_mat_rank(const fmpz_mat_t A)sourceReturns the rank of A over \mathbb{Q}.
For entries of at most (\beta - 4)/2 bits (\beta = FLINT_BITS) the rank is computed by fmpz_mat_rank_small_inplace, integer elimination in single words that falls back to the general code on overflow; otherwise by fmpz_mat_fflu if \min(m, n) < 25 and by fmpz_mat_rref (which then uses the multimodular fmpz_mat_rref_mul) for larger matrices. The result is always exact.
Guides#
Cite this page
The FLINT team, “fmpz_mat_rank (fmpz_mat.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/fmpz_mat/fmpz_mat_rank.html (generated 2026-10-20).
@misc{flint-doc-fmpz-mat-fmpz-mat-rank,
author = {{The FLINT team}},
title = {{fmpz\_mat\_rank (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_rank.html},
note = {Generated 2026-10-20}
}