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
140
141
142
143
144
145
146
147
148
149
150

/*
    Copyright (C) 2020 Daniel Schultz

    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 "fmpz.h"
#include "fmpz_mod.h"
#include "fmpz_mod_poly.h"
#include "fmpz_mod_poly_factor.h"

/* Defined in t-roots.c and t-roots_factored.c */
#define test_poly test_poly_roots
void test_poly(
    fmpz_mod_poly_factor_t roots,
    const fmpz_mod_poly_t f,
    int want_mult,
    const fmpz_mod_ctx_t ctx)
{
    slong i, multiplicity;
    fmpz_mod_poly_t q, qt, r;

    fmpz_mod_poly_init(q, ctx);
    fmpz_mod_poly_init(qt, ctx);
    fmpz_mod_poly_init(r, ctx);
    fmpz_mod_poly_set(q, f, ctx);

    fmpz_mod_poly_roots(roots, f, want_mult, ctx);

    for (i = 0; i < roots->num; i++)
    {
        if (fmpz_mod_poly_degree(roots->poly + i, ctx) != 1)
        {
            flint_printf("FAILED:\ncheck root is linear\n");
            fflush(stdout);
            flint_abort();
        }

        if (!fmpz_is_one(roots->poly[i].coeffs + 1))
        {
            flint_printf("FAILED:\ncheck root is monic\n");
            fflush(stdout);
            flint_abort();
        }

        multiplicity = 0;
        while (fmpz_mod_poly_divrem(qt, r, q, roots->poly + i, ctx),
               fmpz_mod_poly_is_zero(r, ctx))
        {
            fmpz_mod_poly_swap(q, qt, ctx);
            multiplicity++;
        }

        if (multiplicity <= 0)
        {
            flint_printf("FAILED:\ncheck root is a root\n");
            fflush(stdout);
            flint_abort();
        }

        if (roots->exp[i] != (want_mult ? multiplicity : 1))
        {
            flint_printf("FAILED:\ncheck root multiplicity\n");
            fflush(stdout);
            flint_abort();
        }
    }

    fmpz_mod_poly_roots(roots, q, want_mult, ctx);
    if (roots->num > 0)
    {
        flint_printf("FAILED:\ncheck missing roots\n");
        fflush(stdout);
        flint_abort();
    }

    fmpz_mod_poly_clear(q, ctx);
    fmpz_mod_poly_clear(qt, ctx);
    fmpz_mod_poly_clear(r, ctx);
}

TEST_FUNCTION_START(fmpz_mod_poly_factor_roots, state)
{
    slong i, j, k, l;
    fmpz_mod_ctx_t ctx;

    fmpz_mod_ctx_init_ui(ctx, 2);

    for (i = 0; i < 10 * flint_test_multiplier(); i++)
    {
        fmpz_t p;
        fmpz_mod_poly_t f;
        fmpz_mod_poly_factor_t r;

        fmpz_init(p);
        fmpz_randtest_unsigned(p, state, 100);

        fmpz_nextprime(p, p, 1);
        fmpz_mod_ctx_set_modulus(ctx, p);

        fmpz_mod_poly_init(f, ctx);
        fmpz_mod_poly_factor_init(r, ctx);

        for (j = 0; j < 4; j++)
        {
            do {
                fmpz_mod_poly_randtest(f, state, n_randint(state, 20) + 1, ctx);
            } while (fmpz_mod_poly_is_zero(f, ctx));

            for (k = 0; k < 5; k++)
            {
                fmpz_mod_poly_t ff;
                fmpz_mod_poly_init(ff, ctx);
                fmpz_mod_poly_fit_length(ff, 2, ctx);
                fmpz_one(ff->coeffs + 1);
                fmpz_randm(ff->coeffs + 0, state, p);
                ff->length = 2;
                for (l = 1 + n_randint(state, 5); l > 0; l--)
                    fmpz_mod_poly_mul(f, f, ff, ctx);
                fmpz_mod_poly_clear(ff, ctx);
            }

            if (n_randint(state, 2))
            {
                test_poly(r, f, 1, ctx);
                test_poly(r, f, 0, ctx);
            }
            else
            {
                test_poly(r, f, 0, ctx);
                test_poly(r, f, 1, ctx);
            }
        }

        fmpz_mod_poly_factor_clear(r, ctx);
        fmpz_mod_poly_clear(f, ctx);
        fmpz_clear(p);
    }

    fmpz_mod_ctx_clear(ctx);

    TEST_FUNCTION_END(state);
}
#undef test_poly