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
|
# Copyright (c) 1997-2024
# Ewgenij Gawrilow, Michael Joswig, and the polymake team
# Technische Universität Berlin, Germany
# https://polymake.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, or (at your option) any
# later version: http://www.gnu.org/licenses/gpl.txt.
#
# 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.
#-------------------------------------------------------------------------------
object PolyhedralFan<Rational> {
# @category Toric Varieties
# A fan is __Q-GORENSTEIN__ if each maximal cone is [[Cone::Q_GORENSTEIN_CONE|Q_Gorenstein]].
property Q_GORENSTEIN : Bool;
# @category Toric Varieties
# If a fan is [[Q_GORENSTEIN]], then its __Q-Gorenstein index__ is the least common multiple of the [[Cone::Q_GORENSTEIN_CONE_INDEX|Q-Gorenstein indices]] of its maximal cones. Otherwise Q_GORENSTEIN_INDEX is undefined.
property Q_GORENSTEIN_INDEX : Int;
# @category Toric Varieties
# A fan is __Gorenstein__ if it is [[Q_GORENSTEIN]] with [[Q_GORENSTEIN_INDEX]] equal to one.
property GORENSTEIN : Bool;
# @category Toric Varieties
# A fan is __smooth__ if all cones of the fan are [[Cone::SMOOTH_CONE|smooth]].
property SMOOTH_FAN : Bool;
rule Q_GORENSTEIN, Q_GORENSTEIN_INDEX : RAYS, MAXIMAL_CONES, FAN_DIM {
my $r = 1;
foreach (@{$this->MAXIMAL_CONES}) {
my $g = polytope::q_gorenstein_cone($this->RAYS->minor($_,All), $this->FAN_DIM);
if ( !$g->first ) {
$this->Q_GORENSTEIN = false;
return;
} else {
$r = lcm($r, $g->second);
}
}
$this->Q_GORENSTEIN = true;
$this->Q_GORENSTEIN_INDEX = $r;
}
weight 1.10;
rule GORENSTEIN : Q_GORENSTEIN, Q_GORENSTEIN_INDEX {
$this->GORENSTEIN = $this->Q_GORENSTEIN && $this->Q_GORENSTEIN_INDEX == 1;
}
weight 0.1;
rule GORENSTEIN, Q_GORENSTEIN, Q_GORENSTEIN_INDEX : {
$this->GORENSTEIN = true;
$this->Q_GORENSTEIN = true;
$this->Q_GORENSTEIN_INDEX = 1;
}
precondition : SMOOTH_FAN;
weight 0.1;
rule SMOOTH_FAN : RAYS, MAXIMAL_CONES, SIMPLICIAL {
if ( !$this->SIMPLICIAL ) {
$this->SMOOTH_FAN = false;
} else {
my $rays = primitive($this->RAYS);
my $smooth_fan = true;
foreach (@{$this->MAXIMAL_CONES}) {
my $g = 0;
my $m = $rays->minor($_,All);
foreach (@{all_subsets_of_k(sequence(0, $m->cols), $m->rows)}) {
$g = gcd($g, abs(det($m->minor(All,$_))));
last if ($g == 1);
}
$smooth_fan = false, last if $g != 1;
}
$this->SMOOTH_FAN = $smooth_fan;
}
}
weight 1.10;
}
# Local Variables:
# mode: perl
# c-basic-offset:3
# End:
|
