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
|
/**************************************************************************
* *
* Regina - A Normal Surface Theory Calculator *
* Computational Engine *
* *
* Copyright (c) 1999-2008, Ben Burton *
* For further details contact Ben Burton (bab@debian.org). *
* *
* This program is free software; you can redistribute it and/or *
* modify it under the terms of the GNU General Public License as *
* published by the Free Software Foundation; either version 2 of the *
* License, or (at your option) any later version. *
* *
* This program is distributed in the hope that it will be useful, but *
* WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
* General Public License for more details. *
* *
* You should have received a copy of the GNU General Public *
* License along with this program; if not, write to the Free *
* Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, *
* MA 02110-1301, USA. *
* *
**************************************************************************/
/* end stub */
#include "manifold/nsfs.h"
#include "manifold/nsfsaltset.h"
namespace regina {
NSFSAltSet::NSFSAltSet(const NSFSpace* sfs) {
/**
* Note that whenever we add a (1,1) twist, we compensate by setting
* row 2 -> row 2 + row 1 in our conversion matrix.
*/
// Start with the original, reduced to give obstruction constant zero.
data_[0] = new NSFSpace(*sfs);
data_[0]->reduce(false);
long b = data_[0]->obstruction();
if (b)
data_[0]->insertFibre(1, -b);
conversion_[0] = NMatrix2(1, 0, -b, 1);
reflected_[0] = false;
/**
* If the space is M/n2, we can replace it with D:(2,1)(2,-1)
* with fibre and orbifold curves switched. To preserve the
* determinant of the matching matrix we will actually use a
* [0,1,-1,0] switch instead of a [0,1,1,0] switch.
*
* In fact we will use D:(2,1)(2,1) instead, which means:
*
* M_basis = [ 0 1 ] [ 1 0 ] D_basis = [ -1 1 ] D_basis;
* [ -1 0 ] [ -1 1 ] [ -1 0 ]
*
* D_basis = [ 1 0 ] [ 0 -1 ] M_basis = [ 0 -1 ] M_basis.
* [ 1 1 ] [ 1 0 ] [ 1 -1 ]
*/
if (data_[0]->baseClass() == NSFSpace::bn2 &&
data_[0]->baseGenus() == 1 &&
(! data_[0]->baseOrientable()) &&
data_[0]->punctures(false) == 1 &&
data_[0]->punctures(true) == 0 &&
data_[0]->reflectors() == 0 &&
data_[0]->fibreCount() == 0 &&
data_[0]->obstruction() == 0) {
delete data_[0];
data_[0] = new NSFSpace(NSFSpace::bo1, 0 /* genus */,
1 /* punctures */, 0 /* twisted */,
0 /* reflectors */, 0 /* twisted */);
data_[0]->insertFibre(2, 1);
data_[0]->insertFibre(2, 1);
conversion_[0] = NMatrix2(0, -1, 1, -1) * conversion_[0];
}
// Using data_[0] as a foundation, try now for a reflection.
data_[1] = new NSFSpace(*data_[0]);
data_[1]->reflect();
data_[1]->reduce(false);
b = data_[1]->obstruction();
data_[1]->insertFibre(1, -b);
conversion_[1] = NMatrix2(1, 0, -b, -1) * conversion_[0];
reflected_[1] = true;
size_ = 2;
// In the vanilla case, this is all. However, we can occasionally
// do a little more.
// Can we negate all fibres without reflecting?
// Note that (1,2) == (1,0) in this case, so this is only
// interesting if we have an odd number of exceptional fibres.
if (data_[0]->fibreNegating() && (data_[0]->fibreCount() % 2 != 0)) {
// Do it by adding a single (1,1). The subsequent reduce() will
// negate fibres to bring the obstruction constant back down to
// zero, giving the desired effect.
data_[2] = new NSFSpace(*data_[0]);
data_[2]->insertFibre(1, 1);
data_[2]->reduce(false);
b = data_[2]->obstruction();
data_[2]->insertFibre(1, -b);
conversion_[2] = NMatrix2(1, 0, -b + 1, 1) * conversion_[0];
reflected_[2] = false;
// And do it again with an added reflection.
data_[3] = new NSFSpace(*data_[0]);
data_[3]->insertFibre(1, 1);
data_[3]->reflect();
data_[3]->reduce(false);
b = data_[3]->obstruction();
data_[3]->insertFibre(1, -b);
conversion_[3] = NMatrix2(1, 0, -b - 1, -1) * conversion_[0];
reflected_[3] = true;
size_ = 4;
}
}
void NSFSAltSet::deleteAll() {
for (unsigned i = 0; i < size_; i++)
delete data_[i];
}
void NSFSAltSet::deleteAll(NSFSpace* exception) {
for (unsigned i = 0; i < size_; i++)
if (data_[i] != exception)
delete data_[i];
}
void NSFSAltSet::deleteAll(NSFSpace* exception1, NSFSpace* exception2) {
for (unsigned i = 0; i < size_; i++)
if (data_[i] != exception1 && data_[i] != exception2)
delete data_[i];
}
} // namespace regina
|
