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/*
Copyright (C) 2026 Edgar Costa
This file is part of FLINT.
FLINT is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 3 of the License, or
(at your option) any later version. See <https://www.gnu.org/licenses/>.
*/
#include "nmod.h"
#include "nmod_mat.h"
slong
nmod_mat_left_nullspace(nmod_mat_t X, const nmod_mat_t A)
{
slong m = A->r;
slong n = A->c;
slong nullity, i, j;
nmod_mat_t At, Y;
/*
Left nullspace of A equals right nullspace of A^T, expressed
as row vectors. We defer to nmod_mat_nullspace on A^T (which
returns column vectors) and transpose the result.
*/
nmod_mat_init(At, n, m, A->mod.n);
nmod_mat_transpose(At, A);
nmod_mat_init(Y, m, m, A->mod.n);
nullity = nmod_mat_nullspace(Y, At);
nmod_mat_zero(X);
for (i = 0; i < nullity; i++)
for (j = 0; j < m; j++)
nmod_mat_entry(X, i, j) = nmod_mat_entry(Y, j, i);
nmod_mat_clear(Y);
nmod_mat_clear(At);
return nullity;
}