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/*
Copyright (C) 2010 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_factor.h"
#include "fmpz_vec.h"
#include "fmpz_mat.h"
void
fmpz_mat_randdet(fmpz_mat_t mat, flint_rand_t state, const fmpz_t det)
{
slong i, j, k, n;
int parity;
fmpz * diag;
fmpz_factor_t factor;
n = mat->r;
if (n != mat->c)
{
flint_throw(FLINT_ERROR, "Exception (fmpz_mat_randdet). Non-square matrix.\n");
}
if (n < 1)
return;
/* Start with the zero matrix */
fmpz_mat_zero(mat);
if (*det == WORD(0))
return;
fmpz_factor_init(factor);
fmpz_factor(factor, det);
diag = _fmpz_vec_init(n);
for (i = 0; i < n; i++)
fmpz_one(&diag[i]);
/* Form diagonal entries that multiply to the determinant */
for (i = 0; i < factor->num; i++)
{
for (j = 0; j < (slong) factor->exp[i]; j++)
{
k = n_randint(state, n);
fmpz_mul(&diag[k], &diag[k], &factor->p[i]);
}
}
/* Reverse signs an even number of times */
for (i = 0; i < 2*n; i++)
{
k = n_randint(state, n);
fmpz_neg(&diag[k], &diag[k]);
}
if (factor->sign == -1)
fmpz_neg(&diag[0], &diag[0]);
parity = fmpz_mat_randpermdiag(mat, state, diag, n);
/* Need another reversal if the permutation was odd */
if (parity)
{
for (i = 0; i < mat->r; i++)
{
for (j = 0; j < mat->c; j++)
{
if (!fmpz_is_zero(fmpz_mat_entry(mat, i, j)))
{
fmpz_neg(fmpz_mat_entry(mat, i, j), fmpz_mat_entry(mat, i, j));
goto end;
}
}
}
}
end:
_fmpz_vec_clear(diag, n);
fmpz_factor_clear(factor);
}