/*=============================================================================

    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) 2010-2012 Fredrik Johansson
    Copyright (C) 2014 Alex J. Best

******************************************************************************/

#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;
}
