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/*
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_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;
}