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) 2026 Alexey Orlov

    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 "ulong_extras.h"
#include "long_extras.h"
#include "qadic.h"
#include "nmod_poly.h"
#include "fmpz_mod.h"
#include "fmpz_mod_poly.h"

/*
originally it was possible to create qadic context only with conway polynomial
  or, using qadic_ctx_init, with a random irreducible polynomial if it fails

we have two cubic irreducible polynomials over F_2
x^3 + x + 1 (conway polynomial)
x^3 + x^2 + 1
we create 4 qadic contexts:
  1. with conway polynomial, using _qadic_ctx_init_conway_ui
  2. using qadic_ctx_init, which will also use conway polynomial
  3. with nmod_poly_t modulus f = x^3 + x^2 + 1
  4. with fmpz_mod_poly_t modulus f = x^3 + x^2 + 1
for all 4 we compute g^3 + g^2 + 1 and g^3 + g + 1 for a generator g (lift of a generator of the residue field)
*/

static inline void compute_f(qadic_t out, qadic_ctx_t ctx)
{
    qadic_t z, z0, z2, z3, tmp;

    qadic_init(z); qadic_init(z0); qadic_init(z2); qadic_init(z3); qadic_init(tmp);

    qadic_gen(z, ctx); qadic_set_ui(z0, 1, ctx); qadic_mul(z2, z, z, ctx); qadic_mul(z3, z2, z, ctx);
    qadic_add(tmp, z0, z2, ctx);
    qadic_add(out, tmp, z3, ctx);

    qadic_clear(z); qadic_clear(z0); qadic_clear(z2); qadic_clear(z3); qadic_clear(tmp);
}

static inline void compute_f_conway(qadic_t out, qadic_ctx_t ctx)
{
    qadic_t z, z0, z2, z3, tmp;

    qadic_init(z); qadic_init(z0); qadic_init(z2); qadic_init(z3); qadic_init(tmp);

    qadic_gen(z, ctx); qadic_set_ui(z0, 1, ctx); qadic_mul(z2, z, z, ctx); qadic_mul(z3, z2, z, ctx);
    qadic_add(tmp, z0, z, ctx);
    qadic_add(out, tmp, z3, ctx);

    qadic_clear(z); qadic_clear(z0); qadic_clear(z2); qadic_clear(z3); qadic_clear(tmp);
}

static inline void error_exit(const char* prefix, qadic_t val, qadic_ctx_t ctx)
{
    flint_printf("FAIL\n\n");
    flint_printf("%s", prefix), qadic_print_pretty(val, ctx), flint_printf("\n");
    fflush(stdout);
    flint_abort();
}

TEST_FUNCTION_START(qadic_init, state)
{
    fmpz_mod_ctx_t GF;
    nmod_poly_t f_nmod; fmpz_mod_poly_t f;
    qadic_ctx_t ctx_conway; qadic_ctx_t ctx; qadic_ctx_t ctx_f_nmod; qadic_ctx_t ctx_f;
    qadic_t fg_val;
    fmpz_t p;

    fmpz_init(p); fmpz_set_ui(p, 2);

    nmod_poly_init(f_nmod, 2);
    nmod_poly_set_coeff_ui(f_nmod, 0, 1);
    nmod_poly_set_coeff_ui(f_nmod, 2, 1);
    nmod_poly_set_coeff_ui(f_nmod, 3, 1);

    fmpz_mod_ctx_init_ui(GF, 2);
    fmpz_mod_poly_init(f, GF);
    fmpz_mod_poly_set_nmod_poly(f, f_nmod);

    _qadic_ctx_init_conway_ui(ctx_conway, 2, 3, 0, 1, "x", PADIC_SERIES);
    qadic_ctx_init(ctx, p, 3, 0, 1, "x", PADIC_SERIES);
    qadic_ctx_init_modulus_nmod(ctx_f_nmod, 2, f_nmod, 0, 1, "x", PADIC_SERIES);
    qadic_ctx_init_modulus(ctx_f, p, f, 0, 1, "x", PADIC_SERIES);

    qadic_init(fg_val);

    compute_f(fg_val, ctx_conway);
    if (qadic_is_zero(fg_val))
        error_exit("conway: g^3 + g^2 + 1 = ", fg_val, ctx_conway);

    compute_f_conway(fg_val, ctx_conway);
    if (!qadic_is_zero(fg_val))
        error_exit("conway: g^3 + g + 1 = ", fg_val, ctx_conway);

    compute_f(fg_val, ctx);
    if (qadic_is_zero(fg_val))
        error_exit("default: g^3 + g^2 + 1 = ", fg_val, ctx);

    compute_f_conway(fg_val, ctx);
    if (!qadic_is_zero(fg_val))
        error_exit("default: g^3 + g + 1 = ", fg_val, ctx);

    compute_f(fg_val, ctx_f);
    if (!qadic_is_zero(fg_val))
        error_exit("f_fmpz: g^3 + g^2 + 1 = ", fg_val, ctx_f);

    compute_f_conway(fg_val, ctx_f);
    if (qadic_is_zero(fg_val))
        error_exit("f_fmpz: g^3 + g + 1 = ", fg_val, ctx_f);

    compute_f(fg_val, ctx_f_nmod);
    if (!qadic_is_zero(fg_val))
        error_exit("f_nmod: g^3 + g^2 + 1 = ", fg_val, ctx_f_nmod);

    compute_f_conway(fg_val, ctx_f_nmod);
    if (qadic_is_zero(fg_val))
        error_exit("f_nmod: g^3 + g + 1 = ", fg_val, ctx_f_nmod);

    qadic_clear(fg_val);
    qadic_ctx_clear(ctx_conway);
    qadic_ctx_clear(ctx);
    qadic_ctx_clear(ctx_f_nmod);
    qadic_ctx_clear(ctx_f);
    nmod_poly_clear(f_nmod);
    fmpz_mod_poly_clear(f, GF);
    fmpz_mod_ctx_clear(GF);
    fmpz_clear(p);

    TEST_FUNCTION_END(state);
}