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/*
Copyright (C) 2015 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 "acb_poly.h"
void
_acb_poly_root_bound_fujiwara(mag_t bound, acb_srcptr poly, slong len)
{
mag_t t, u, v;
slong i;
if (len <= 1)
{
mag_inf(bound);
return;
}
mag_init(t);
mag_init(u);
mag_init(v);
/* u = 1/leading */
acb_get_mag_lower(t, poly + len - 1);
mag_one(u);
mag_div(u, u, t);
mag_zero(v);
for (i = 0; i < len - 1; i++)
{
acb_get_mag(t, poly + len - 2 - i);
mag_mul(t, t, u);
if (i == len - 2)
mag_mul_2exp_si(t, t, -1);
mag_root(t, t, i + 1);
mag_max(v, v, t);
}
mag_mul_2exp_si(bound, v, 1);
mag_clear(t);
mag_clear(u);
mag_clear(v);
}
void
acb_poly_root_bound_fujiwara(mag_t bound, acb_poly_t poly)
{
_acb_poly_root_bound_fujiwara(bound, poly->coeffs, poly->length);
}