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

/*
    Copyright (C) 2011 William Hart
    Copyright (C) 2012 Andres Goens
    Copyright (C) 2013 Mike Hansen
    Copyright (C) 2020, 2025 Fredrik Johansson

    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 "gr_poly.h"

/* assumes lenA >= lenB >= 1, and both A and B have nonzero leading
   coefficient */
int
_gr_poly_gcd_generic(gr_ptr G, slong * lenG, gr_srcptr A, slong lenA,
                                gr_srcptr B, slong lenB, gr_ctx_t ctx)
{
    /* todo:
        * extract powers of x (see fmpz_poly_gcd)
        * automaticically use hgcd at least over finite fields
        * gcd_euclidean shouldn't actually be used over fields with fractions.
          instead, we want to clear denominators and call the subresultant
          algorithm.
    */
    if (gr_ctx_is_field(ctx) == T_TRUE)
    {
        return _gr_poly_gcd_euclidean(G, lenG, A, lenA, B, lenB, ctx);
    }
    else if (gr_ctx_is_unique_factorization_domain(ctx) == T_TRUE)
    {
        return _gr_poly_gcd_subresultant(G, lenG, A, lenA, B, lenB, ctx);
    }
    else
    {
        *lenG = 0;
        return GR_UNABLE;
    }
}

int
gr_poly_gcd_wrapper(gr_method_poly_gcd_op gcd_impl, int canonicalise_unit, gr_poly_t G, const gr_poly_t A,
                        const gr_poly_t B, gr_ctx_t ctx)
{
    slong lenA = A->length, lenB = B->length, lenG;
    slong sz = ctx->sizeof_elem;
    gr_ptr g;
    int status;

    if (A->length == 0 && B->length == 0)
        return gr_poly_zero(G, ctx);

    if (A->length == 0)
        return canonicalise_unit ? gr_poly_canonical_associate(G, NULL, B, ctx) : gr_set(G, B, ctx);

    if (B->length == 0)
        return canonicalise_unit ? gr_poly_canonical_associate(G, NULL, A, ctx) : gr_set(G, A, ctx);

    if (A->length < B->length)
        return gr_poly_gcd_wrapper(gcd_impl, canonicalise_unit, G, B, A, ctx);

    if (gr_is_zero(GR_ENTRY(A->coeffs, A->length - 1, sz), ctx) != T_FALSE ||
        gr_is_zero(GR_ENTRY(B->coeffs, B->length - 1, sz), ctx) != T_FALSE)
    {
        return GR_UNABLE;
    }

    /* lenA >= lenB >= 1 */
    if (G == A || G == B)
    {
        g = flint_malloc(FLINT_MIN(lenA, lenB) * sz);
        _gr_vec_init(g, FLINT_MIN(lenA, lenB), ctx);
    }
    else
    {
        gr_poly_fit_length(G, FLINT_MIN(lenA, lenB), ctx);
        g = G->coeffs;
    }

    status = gcd_impl(g, &lenG, A->coeffs, lenA, B->coeffs, lenB, ctx);

    if (G == A || G == B)
    {
        _gr_vec_clear(G->coeffs, G->alloc, ctx);
        flint_free(G->coeffs);
        G->coeffs = g;
        G->alloc = FLINT_MIN(lenA, lenB);
        G->length = FLINT_MIN(lenA, lenB);
    }
    _gr_poly_set_length(G, lenG, ctx);

    if (status == GR_SUCCESS && lenG != 0 && canonicalise_unit)
    {
        status = gr_poly_canonical_associate(G, NULL, G, ctx);
    }

    return status;
}


int
gr_poly_gcd(gr_poly_t G, const gr_poly_t A,
                        const gr_poly_t B, gr_ctx_t ctx)
{
    return gr_poly_gcd_wrapper((gr_method_poly_gcd_op) _gr_poly_gcd, 1, G, A, B, ctx);
}