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

/*
    Copyright (C) 2020 Fredrik Johansson
    Copyright (C) 2025 Andrii Yanovets
    
    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 "fmpz.h"
#include "fmpz_mod_mpoly.h"

static int
monomial_divides(const ulong * exp1, const ulong * exp2, slong nvars)
{
    slong i;
    for (i = 0; i < nvars; i++)
        if (exp1[i] > exp2[i])
            return 0;
    return 1;
}

void
fmpz_mod_mpoly_vec_autoreduction_groebner(fmpz_mod_mpoly_vec_t G, const fmpz_mod_mpoly_vec_t Gin, const fmpz_mod_mpoly_ctx_t ctx)
{
    slong i, j, nvars;
    ulong * exp1, * exp2;

    if (G != Gin)
        fmpz_mod_mpoly_vec_set(G, Gin, ctx);

    /* Content removal */
    for (i = 0; i < G->length; i++)
        fmpz_mod_mpoly_make_monic(fmpz_mod_mpoly_vec_entry(G, i), fmpz_mod_mpoly_vec_entry(G, i), ctx);
    
    /* Make sure there are no duplicate or zero entries */
    for (i = 0; i < G->length; i++)
    {
        if (fmpz_mod_mpoly_is_zero(fmpz_mod_mpoly_vec_entry(G, i), ctx))
        {
            fmpz_mod_mpoly_swap(fmpz_mod_mpoly_vec_entry(G, i), fmpz_mod_mpoly_vec_entry(G, G->length - 1), ctx);
            fmpz_mod_mpoly_vec_set_length(G, G->length - 1, ctx);
        }
        else
        {
            for (j = i + 1; j < G->length; j++)
            {
                if (fmpz_mod_mpoly_equal(fmpz_mod_mpoly_vec_entry(G, i), fmpz_mod_mpoly_vec_entry(G, j), ctx))
                {
                    fmpz_mod_mpoly_swap(fmpz_mod_mpoly_vec_entry(G, j), fmpz_mod_mpoly_vec_entry(G, G->length - 1), ctx);
                    fmpz_mod_mpoly_vec_set_length(G, G->length - 1, ctx);
                }
            }
        }
    }

    if (G->length <= 1)
        return;

    /* First filter based on divisibility of leading terms */

    nvars = ctx->minfo->nvars;
    exp1 = flint_malloc(nvars * sizeof(ulong));
    exp2 = flint_malloc(nvars * sizeof(ulong));

    for (i = 0; i < G->length; i++)
    {
        fmpz_mod_mpoly_get_term_exp_ui(exp1, fmpz_mod_mpoly_vec_entry(G, i), 0, ctx);

        for (j = 0; j < G->length; j++)
        {
            if (i != j)
            {
                fmpz_mod_mpoly_get_term_exp_ui(exp2, fmpz_mod_mpoly_vec_entry(G, j), 0, ctx);

                if (monomial_divides(exp2, exp1, nvars))
                {
                    fmpz_mod_mpoly_swap(fmpz_mod_mpoly_vec_entry(G, i), fmpz_mod_mpoly_vec_entry(G, G->length - 1), ctx);
                    fmpz_mod_mpoly_vec_set_length(G, G->length - 1, ctx);
                    break;
                }
            }
        }
    }

    flint_free(exp1);
    flint_free(exp2);

    /* Now do inter-reduction */
    if (G->length >= 2)
    {
        fmpz_t scale;
        fmpz_mod_mpoly_struct ** Q, ** B;
        slong i, j, alloc;

        alloc = G->length - 1;

        fmpz_init(scale);
        Q = flint_malloc(sizeof(fmpz_mod_mpoly_struct *) * alloc);
        B = flint_malloc(sizeof(fmpz_mod_mpoly_struct *) * alloc);

        for (i = 0; i < alloc; i++)
        {
            Q[i] = flint_malloc(sizeof(fmpz_mod_mpoly_struct));
            fmpz_mod_mpoly_init(Q[i], ctx);
        }

        for (i = 0; i < G->length; i++)
        {
            for (j = 0; j < i; j++)
                B[j] = fmpz_mod_mpoly_vec_entry(G, j);
            for (j = i + 1; j < G->length; j++)
                B[j - 1] = fmpz_mod_mpoly_vec_entry(G, j);

            fmpz_mod_mpoly_divrem_ideal(Q, fmpz_mod_mpoly_vec_entry(G, i), fmpz_mod_mpoly_vec_entry(G, i), B, G->length - 1, ctx);
            if (!fmpz_mod_mpoly_is_zero(fmpz_mod_mpoly_vec_entry(G, i), ctx))
                fmpz_mod_mpoly_make_monic(fmpz_mod_mpoly_vec_entry(G, i), fmpz_mod_mpoly_vec_entry(G, i), ctx);

            if (fmpz_mod_mpoly_is_zero(fmpz_mod_mpoly_vec_entry(G, i), ctx))
            {
                fmpz_mod_mpoly_swap(fmpz_mod_mpoly_vec_entry(G, i), fmpz_mod_mpoly_vec_entry(G, G->length - 1), ctx);
                fmpz_mod_mpoly_vec_set_length(G, G->length - 1, ctx);
                i--;
            }
        }

        for (i = 0; i < alloc; i++)
        {
            fmpz_mod_mpoly_clear(Q[i], ctx);
            flint_free(Q[i]);
        }

        flint_free(Q);
        flint_free(B);
        fmpz_clear(scale);
    }
}