File: is_in_hnf.c

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flint 2.5.2-19
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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) 2014 Alex J. Best

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

#include "fmpz_mat.h"

int fmpz_mat_is_in_hnf(const fmpz_mat_t A)
{
    slong i, last_i, j, prev_j;

    /* find last non-zero row */
    for (last_i = A->r - 1; last_i >= 0; last_i--)
    {
        for (j = 0; j < A->c; j++)
        {
            if (!fmpz_is_zero(fmpz_mat_entry(A, last_i, j)))
                break;
        }
        if (j < A->c)
            break;
    }

    /* hermite form structure */
    prev_j = -1;
    for (i = 0; i <= last_i; i++)
    {
        slong i2;

        for (j = 0; j < A->c; j++)
        {
            if (!fmpz_is_zero(fmpz_mat_entry(A, i, j)))
            {
                if (fmpz_sgn(fmpz_mat_entry(A, i, j)) < 0)
                    return 0;
                break;
            }
        }
        if (j == A->c || j <= prev_j)
            return 0;
        prev_j = j;
        for (i2 = 0; i2 < i; i2++)
        {
            if (fmpz_cmp(fmpz_mat_entry(A, i2, j), fmpz_mat_entry(A, i, j)) >= 0)
                return 0;
            if (fmpz_sgn(fmpz_mat_entry(A, i2, j)) < 0)
                return 0;
        }
    }

    return 1;
}