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
/*
Copyright (C) 2011 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 "test_helpers.h"
#include "ulong_extras.h"
#include "nmod_mat.h"
TEST_FUNCTION_START(nmod_mat_nullspace, state)
{
slong i;
for (i = 0; i < 1000 * flint_test_multiplier(); i++)
{
nmod_mat_t A, B, ker;
ulong mod;
slong m, n, d, r, nullity, nulrank;
m = n_randint(state, 30);
n = n_randint(state, 30);
for (r = 0; r <= FLINT_MIN(m,n); r++)
{
mod = n_randtest_prime(state, 0);
d = n_randint(state, 2*m*n + 1);
nmod_mat_init(A, m, n, mod);
nmod_mat_init(ker, n, n, mod);
nmod_mat_init(B, m, n, mod);
nmod_mat_randrank(A, state, r);
/* Densify */
if (n_randlimb(state) % 2)
nmod_mat_randops(A, state, d);
nullity = nmod_mat_nullspace(ker, A);
nulrank = nmod_mat_rank(ker);
if (nullity != nulrank)
TEST_FUNCTION_FAIL(
"rank(ker) != nullity\n"
"A = %{nmod_mat}\n",
A);
if (nullity + r != n)
TEST_FUNCTION_FAIL(
"nullity + rank != n\n"
"A = %{nmod_mat}\n",
A);
nmod_mat_mul(B, A, ker);
if (nmod_mat_rank(B) != 0)
TEST_FUNCTION_FAIL(
"A * ker != 0\n"
"A = %{nmod_mat}\n",
A);
nmod_mat_clear(A);
nmod_mat_clear(ker);
nmod_mat_clear(B);
}
}
TEST_FUNCTION_END(state);
}