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/*
Copyright (C) 2011 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"
void
fmpz_mat_solve_bound(fmpz_t N, fmpz_t D,
const fmpz_mat_t A, const fmpz_mat_t B)
{
slong i, j, m, n;
fmpz_t t, u;
m = B->r;
n = B->c;
fmpz_mat_det_bound(D, A);
fmpz_init(t);
fmpz_init(u);
fmpz_zero(t);
/* Largest column norm of B */
for (j = 0; j < n; j++)
{
fmpz_zero(u);
for (i = 0; i < m; i++)
fmpz_addmul(u, fmpz_mat_entry(B, i, j), fmpz_mat_entry(B, i, j));
if (fmpz_cmp(t, u) < 0)
fmpz_set(t, u);
}
fmpz_sqrtrem(t, u, t);
if (!fmpz_is_zero(u))
fmpz_add_ui(t, t, UWORD(1));
fmpz_mul(N, D, t);
fmpz_clear(t);
fmpz_clear(u);
}