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

/*
    Copyright (C) 2011 Fredrik Johansson
    Copyright (C) 2012 Sebastian Pancratz

    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_poly.h"
#include "fmpz_mat.h"

TEST_FUNCTION_START(fmpz_mat_charpoly, state)
{
    slong m, n, rep, i;

    for (rep = 0; rep < 1000 * flint_test_multiplier(); rep++)
    {
        fmpz_mat_t A, B, C, D;
        fmpz_poly_t f, g;

        m = n_randint(state, 5);
        n = m;

        fmpz_mat_init(A, m, n);
        fmpz_mat_init(B, m, n);
        fmpz_mat_init(C, m, m);
        fmpz_mat_init(D, n, n);
        fmpz_poly_init(f);
        fmpz_poly_init(g);

        fmpz_poly_randtest(f, state, 10, 100);
        fmpz_poly_randtest(g, state, 10, 100);

        fmpz_mat_randtest(A, state, 10);
        fmpz_mat_randtest(B, state, 10);

        fmpz_mat_mul(C, A, B);
        fmpz_mat_mul(D, B, A);

        fmpz_mat_charpoly(f, C);
        fmpz_mat_charpoly(g, D);

        if (!fmpz_poly_equal(f, g))
        {
            flint_printf("FAIL: charpoly(AB) != charpoly(BA).\n");
            flint_printf("Matrix A:\n"), fmpz_mat_print(A), flint_printf("\n");
            flint_printf("Matrix B:\n"), fmpz_mat_print(B), flint_printf("\n");
            flint_printf("cp(AB) = "), fmpz_poly_print_pretty(f, "X"), flint_printf("\n");
            flint_printf("cp(BA) = "), fmpz_poly_print_pretty(g, "X"), flint_printf("\n");
            fflush(stdout);
            flint_abort();
        }

        fmpz_mat_clear(A);
        fmpz_mat_clear(B);
        fmpz_mat_clear(C);
        fmpz_mat_clear(D);
        fmpz_poly_clear(f);
        fmpz_poly_clear(g);
    }

    for (rep = 0; rep < 1000 * flint_test_multiplier(); rep++)
    {
        fmpz_t c;
        fmpz_mat_t A, B;
        fmpz_poly_t f, g;

        m = n_randint(state, 5);
        n = m;

        fmpz_init(c);
        fmpz_mat_init(A, m, n);
        fmpz_mat_init(B, m, n);
        fmpz_poly_init(f);
        fmpz_poly_init(g);

        fmpz_poly_randtest(f, state, 10, 100);
        fmpz_poly_randtest(g, state, 10, 100);

        fmpz_mat_randtest(A, state, 10);
        fmpz_mat_set(B, A);

        for (i = 0; i < 10; i++)
        {
           fmpz_randtest(c, state, 5);
           fmpz_mat_similarity(B, n_randint(state, m), c);
        }

        fmpz_mat_charpoly(f, A);
        fmpz_mat_charpoly(g, B);

        if (!fmpz_poly_equal(f, g))
        {
            flint_printf("FAIL: charpoly(A) != charpoly(P^{-1}AP).\n");
            flint_printf("Matrix A:\n"), fmpz_mat_print(A), flint_printf("\n");
            flint_printf("Matrix P^{-1}AP:\n"), fmpz_mat_print(B), flint_printf("\n");
            flint_printf("cp(A) = "), fmpz_poly_print_pretty(f, "X"), flint_printf("\n");
            flint_printf("cp(P^{-1}AP) = "), fmpz_poly_print_pretty(g, "X"), flint_printf("\n");
            fflush(stdout);
            flint_abort();
        }

        fmpz_clear(c);
        fmpz_mat_clear(A);
        fmpz_mat_clear(B);
        fmpz_poly_clear(f);
        fmpz_poly_clear(g);
    }

    TEST_FUNCTION_END(state);
}