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
62
63
64
65
66
67
68
69
70
71
72
73
74
75
|
/*
Copyright (C) 2017 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 "acb_elliptic.h"
#include "acb_modular.h"
void
acb_elliptic_roots(acb_t e1, acb_t e2, acb_t e3, const acb_t tau, slong prec)
{
acb_t t1, t2, t3, t4;
int e1r, e23r;
if (!arb_is_positive(acb_imagref(tau)) || !arb_is_finite(acb_realref(tau)))
{
acb_indeterminate(e1);
acb_indeterminate(e2);
acb_indeterminate(e3);
return;
}
acb_init(t1);
acb_init(t2);
acb_init(t3);
acb_init(t4);
e1r = e23r = 0;
if (arb_is_int(acb_realref(tau)))
e1r = e23r = 1;
else if (arb_is_int_2exp_si(acb_realref(tau), -1))
e1r = 1;
acb_modular_theta(t1, t2, t3, t4, t1, tau, prec);
acb_pow_ui(t2, t2, 4, prec);
acb_pow_ui(t4, t4, 4, prec);
acb_sub(e2, t2, t4, prec);
acb_mul_2exp_si(t3, t4, 1);
acb_add(e1, t2, t3, prec);
acb_mul_2exp_si(t3, t2, 1);
acb_add(e3, t3, t4, prec);
acb_const_pi(t3, prec);
acb_mul(t3, t3, t3, prec);
acb_div_ui(t3, t3, 3, prec);
acb_mul(e1, e1, t3, prec);
acb_mul(e2, e2, t3, prec);
acb_mul(e3, e3, t3, prec);
acb_neg(e3, e3);
if (e1r)
arb_zero(acb_imagref(e1));
if (e23r)
{
arb_zero(acb_imagref(e2));
arb_zero(acb_imagref(e3));
}
acb_clear(t1);
acb_clear(t2);
acb_clear(t3);
acb_clear(t4);
}
|
