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/*=============================================================================
This file is part of FLINT.
FLINT is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
FLINT is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with FLINT; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
=============================================================================*/
/******************************************************************************
Copyright (C) 2011 Fredrik Johansson
******************************************************************************/
#include "flint.h"
#include "nmod_poly.h"
#include "nmod_poly_mat.h"
long
nmod_poly_mat_nullspace(nmod_poly_mat_t res, const nmod_poly_mat_t mat)
{
long i, j, k, m, n, rank, nullity;
long * pivots;
long * nonpivots;
nmod_poly_mat_t tmp;
nmod_poly_t den;
m = mat->r;
n = mat->c;
nmod_poly_init(den, nmod_poly_mat_modulus(mat));
nmod_poly_mat_init_set(tmp, mat);
rank = nmod_poly_mat_rref(tmp, den, NULL, tmp);
nullity = n - rank;
nmod_poly_mat_zero(res);
if (rank == 0)
{
for (i = 0; i < nullity; i++)
nmod_poly_one(res->rows[i] + i);
}
else if (nullity)
{
pivots = flint_malloc(rank * sizeof(long));
nonpivots = flint_malloc(nullity * sizeof(long));
for (i = j = k = 0; i < rank; i++)
{
while (nmod_poly_is_zero(tmp->rows[i] + j))
{
nonpivots[k] = j;
k++;
j++;
}
pivots[i] = j;
j++;
}
while (k < nullity)
{
nonpivots[k] = j;
k++;
j++;
}
nmod_poly_set(den, tmp->rows[0] + pivots[0]);
for (i = 0; i < nullity; i++)
{
for (j = 0; j < rank; j++)
nmod_poly_set(res->rows[pivots[j]] + i,
tmp->rows[j] + nonpivots[i]);
nmod_poly_neg(res->rows[nonpivots[i]] + i, den);
}
flint_free(pivots);
flint_free(nonpivots);
}
nmod_poly_clear(den);
nmod_poly_mat_clear(tmp);
return nullity;
}
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