gr_mat_nullspace, gr_mat_nullspace_no_resize
#include <flint/gr_mat.h>Set the columns of X to a basis of the right nullspace \{x : Ax = 0\} of the m \times n matrix A, read off from the reduced row echelon form: one basis vector per non-pivot column. gr_mat_nullspace resizes X to n rows and as many columns as the nullity; the no_resize version requires X with n rows and at least that many columns, zero-pads the rest and writes the nullity to nullity.
The basis is not canonical. Over an integral domain that is not a field the basis is computed from gr_mat_rref_den and has entries in the ring; it is a basis over the fraction field. Over other rings the result may be meaningless.
Guides#
The FLINT team, “gr_mat_nullspace, gr_mat_nullspace_no_resize (gr_mat.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/gr_mat/gr_mat_nullspace.html (generated 2026-10-20).
@misc{flint-doc-gr-mat-gr-mat-nullspace,
author = {{The FLINT team}},
title = {{gr\_mat\_nullspace, gr\_mat\_nullspace\_no\_resize (gr\_mat.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/gr_mat/gr_mat_nullspace.html},
note = {Generated 2026-10-20}
}