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/*
Copyright (C) 2011 Fredrik Johansson
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_nullspace(nmod_mat_t X, const nmod_mat_t A)
{
slong i, j, k, m, n, rank, nullity;
slong * p;
slong * pivots;
slong * nonpivots;
nmod_mat_t tmp;
m = A->r;
n = A->c;
p = flint_malloc(sizeof(slong) * FLINT_MAX(m, n));
nmod_mat_init_set(tmp, A);
rank = nmod_mat_rref(tmp);
nullity = n - rank;
nmod_mat_zero(X);
if (rank == 0)
{
for (i = 0; i < nullity; i++)
nmod_mat_entry(X, i, i) = UWORD(1);
}
else if (nullity)
{
pivots = p; /* length = rank */
nonpivots = p + rank; /* length = nullity */
for (i = j = k = 0; i < rank; i++)
{
while (nmod_mat_entry(tmp, i, j) == UWORD(0))
{
nonpivots[k] = j;
k++;
j++;
}
pivots[i] = j;
j++;
}
while (k < nullity)
{
nonpivots[k] = j;
k++;
j++;
}
for (i = 0; i < nullity; i++)
{
for (j = 0; j < rank; j++)
{
ulong c = nmod_mat_entry(tmp, j, nonpivots[i]);
nmod_mat_entry(X, pivots[j], i) = nmod_neg(c, A->mod);
}
nmod_mat_entry(X, nonpivots[i], i) = UWORD(1);
}
}
flint_free(p);
nmod_mat_clear(tmp);
return nullity;
}