1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
|
/*
Copyright (C) 2015 Fredrik Johansson
This file is part of Arb.
Arb 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 2.1 of the License, or
(at your option) any later version. See <http://www.gnu.org/licenses/>.
*/
#include "arb_poly.h"
void
_arb_poly_root_bound_fujiwara(mag_t bound, arb_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 */
arb_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++)
{
arb_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
arb_poly_root_bound_fujiwara(mag_t bound, arb_poly_t poly)
{
_arb_poly_root_bound_fujiwara(bound, poly->coeffs, poly->length);
}
|
