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/*
Copyright (C) 2010-2012 Fredrik Johansson
Copyright (C) 2014 Alex J. Best
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 "fmpz.h"
#include "fmpz_mat.h"
int fmpz_mat_is_in_rref_with_rank(const fmpz_mat_t A, const fmpz_t den, slong rank)
{
slong i, j, k, prev_pivot;
/* bottom should be zero */
for (i = rank; i < A->r; i++)
for (j = 0; j < A->c; j++)
if (!fmpz_is_zero(fmpz_mat_entry(A, i, j)))
return 0;
prev_pivot = -1;
for (i = 0; i < rank; i++)
{
for (j = 0; j < A->c; j++)
{
if (!fmpz_is_zero(fmpz_mat_entry(A, i, j)))
{
/* pivot should have a higher column index than previous */
if (j <= prev_pivot)
return 0;
/* column should be 0 ... 0 1 0 ... 0 */
for (k = 0; k < rank; k++)
{
if (i == k && !fmpz_equal(fmpz_mat_entry(A, k, j), den))
return 0;
if (i != k && !fmpz_is_zero(fmpz_mat_entry(A, k, j)))
return 0;
}
prev_pivot = j;
break;
}
}
}
return 1;
}