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/*
Copyright (C) 2014 Fredrik Johansson
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_hadamard(const fmpz_mat_t A)
{
slong i, j, n;
fmpz_mat_t B, C;
int result;
n = fmpz_mat_nrows(A);
if (n != fmpz_mat_ncols(A))
return 0;
if (n > 2 && n % 4 != 0)
return 0;
for (i = 0; i < n; i++)
for (j = 0; j < n; j++)
if (!fmpz_is_pm1(fmpz_mat_entry(A, i, j)))
return 0;
fmpz_mat_init(B, n, n);
fmpz_mat_init(C, n, n);
fmpz_mat_transpose(B, A);
fmpz_mat_mul(C, A, B);
result = 1;
for (i = 0; i < n && result; i++)
for (j = 0; j < n && result; j++)
result = (*fmpz_mat_entry(C, i, j) == n * (i == j));
fmpz_mat_clear(B);
fmpz_mat_clear(C);
return result;
}