flint-sys 0.9.0

Bindings to the FLINT C library
Documentation 
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
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139

/*
    Copyright (C) 2016 Pascal Molin

    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 "test_helpers.h"
#include "acb_dirichlet.h"

#define nq 5
#define nx 3

TEST_FUNCTION_START(acb_dirichlet_l_hurwitz, state)
{
    slong i, j;
    ulong q[nq] = {3, 5, 61, 91, 800};
    ulong m[nq] = {2, 4, 11, 2, 3};
    slong prec = 150;

    acb_ptr x;
    /* cannot test at s = 1 with hurwitz */
    const char * x_r[nx] = { "1", "0.5", "0.5" };
    const char * x_i[nx] = { "1", "0", "6" };

    acb_t ref, res;
    /*
    default(realprecision, 54)
    X = [ 1 + I, 1/2, 1/2 + 6 * I ]
    C = [Mod(2,3),Mod(4,5),Mod(11,61),Mod(2,91),Mod(3,800)]
    v = concat([ [lfun(c,x) | x<-X] | c<-C])
    apply(z->printf("\"%s\",\n",real(z)),v)
    apply(z->printf("\"%s\",\n",imag(z)),v)
    */
    const char * ref_r[nq * nx] = {
        "0.655527984002548033786648216345221087939439503905627469",
        "0.480867557696828626181220063235589877776829730832371863",
        "1.56831301727577320813799211138797101541772722814204757",
        "0.521271244517346991221550773660594765406476858135844321",
        "0.231750947504015755883383661760877226427886696409005898",
        "0.275543455389521803395512886745330595086898302178508437",
        "0.598221809458540554839300433683735304093606595684903281",
        "0.489264190003695740292779374874163221990017067040417393",
        "0.573331076412428980263984182365365715292560207445592018",
        "0.510279695870740409778738767334484809708615155539404548",
        "0.635626509594367380604827545000418331455019188562281349",
        "0.129304857274642475564179442785425797926079767522671163",
        "1.18088858810025653590356481638012816019876881487868657",
        "2.17175778983760437737667738885959799183430688287297767",
        "3.41568550810774629867945639900431994221065497147578087"
    };
    const char * ref_i[nq * nx] = {
        "0.220206044893215842652155131408935133596486560067476474",
        "0",
        "-0.969458654385732175077973304161399773236957587792986099",
        "0.354614573267731219242838516784605303288232150760467423",
        "0",
        "-0.995392028773643947872231871832838543767598301887892796",
        "1.04370497561090171487193145841005574472705644411957863",
        "-0.108902811943905225853677097712717212629591264759957602",
        "-0.232114369998608907337769019848201890558327186146689311",
        "-0.133300066189980774635445078240315148544665020358019145",
        "0.0119464572932630291870372694406253796888930803905106876",
        "-0.567660589679294457801153713636532209809112025502518666",
        "-0.654079942571300523223917775358845549990877148918886474",
        "0.970337207245832214408380510793679653538607483205616894",
        "-1.43652482351673593824956935036654893593947145947637807"
    };

    x = _acb_vec_init(nx);

    for (j = 0; j < nx; j++)
    {
        if (arb_set_str(acb_realref(x + j), x_r[j], prec) ||
            arb_set_str(acb_imagref(x + j), x_i[j], prec) )
        {
            flint_printf("error while setting x[%wd] <- %s+I*%s\n",
                    j, x_r[j], x_i[j]);
            flint_abort();
        }

    }

    acb_init(ref);
    acb_init(res);

    for (i = 0; i < nq; i++)
    {
        dirichlet_group_t G;
        dirichlet_char_t chi;

        dirichlet_group_init(G, q[i]);
        dirichlet_char_init(chi, G);

        dirichlet_char_log(chi, G, m[i]);

        for (j = 0; j < nx; j++)
        {

            if (arb_set_str(acb_realref(ref), ref_r[i * nx + j], prec - 10) ||
                    arb_set_str(acb_imagref(ref), ref_i[i * nx + j], prec - 10) )
            {
                flint_printf("error while setting ref <- %s+I*%s\n",
                        ref_r[i * nx + j], ref_i[i * nx + j]);
                flint_abort();
            }

            acb_dirichlet_l_hurwitz(res, x + j, NULL, G, chi, prec + 10);

            if (!acb_contains(ref, res))
            {
                    flint_printf("FAIL:\n\n");
                    flint_printf("q = %wu\n", q[i]);
                    flint_printf("m = %wu\n", m[i]);
                    flint_printf("x = ");
                    acb_printd(x, 54);
                    flint_printf("\nref = ");
                    acb_printd(ref, 54);
                    flint_printf("\nl(chi,x) = ");
                    acb_printd(res, 54);
                    flint_printf("\n\n");
                    flint_abort();
            }

        }
        dirichlet_char_clear(chi);
        dirichlet_group_clear(G);

    }
    acb_clear(ref);
    acb_clear(res);
    _acb_vec_clear(x, nx);

    TEST_FUNCTION_END(state);
}