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
149
150
151
152
153
154
155
156
157
158
159
160
161
162
|
# 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 polytope::Polytope {
# @category Unbounded polyhedra
# Bounded subcomplex.
# Defined as the bounded cells of the boundary of the pointed part of the polytope.
# Therefore it only depends on [[VERTICES_IN_FACETS]] and [[FAR_FACE]].
property BOUNDED_COMPLEX : PolyhedralComplex<Scalar> {
# @category Unbounded polyhedra
# For every row of [[VERTICES]] this indicates the corresponding row in the
# [[VERTICES]] of the parent polytope.
property VERTEX_MAP : Array<Int>;
property GRAPH {
# Each edge indicates the maximal dimension of a bounded
# face containing it. Mainly used for visualization purposes.
property EDGE_COLORS : EdgeMap<Undirected,Int> : construct(ADJACENCY);
# Difference of the vertices for each edge (only defined up to signs).
property EDGE_DIRECTIONS : EdgeMap<Undirected,Vector<Scalar>> : construct(ADJACENCY);
# The length of each edge measured in the maximum metric.
property EDGE_LENGTHS : EdgeMap<Undirected,Scalar> : construct(ADJACENCY);
# Sum of all [[EDGE_LENGTHS]].
property TOTAL_LENGTH : Scalar;
}
}
rule BOUNDED_COMPLEX.GRAPH.NodePerm.PERMUTATION = VertexPerm.PERMUTATION;
rule BOUNDED_COMPLEX.GRAPH.ADJACENCY : GRAPH.ADJACENCY, FAR_FACE, BOUNDED_COMPLEX.VERTEX_MAP, N_VERTICES {
my $g = permuted_inv_nodes(new GraphAdjacency(induced_subgraph($this->GRAPH->ADJACENCY, ~ $this->FAR_FACE)), map_vertices_down($this->BOUNDED_COMPLEX->VERTEX_MAP, $this->N_VERTICES) );
$g->squeeze;
$this->BOUNDED_COMPLEX->GRAPH->ADJACENCY = $g;
}
precondition : !BOUNDED;
weight 1.20;
rule BOUNDED_COMPLEX.GRAPH.ADJACENCY = GRAPH.ADJACENCY;
precondition : BOUNDED;
rule BOUNDED_COMPLEX.GRAPH.EDGE_COLORS : BOUNDED_COMPLEX.MAXIMAL_POLYTOPES_COMBINATORIAL_DIMS, BOUNDED_COMPLEX.MAXIMAL_POLYTOPES, BOUNDED_COMPLEX.GRAPH.ADJACENCY, BOUNDED_COMPLEX.GRAPH.N_EDGES {
polytope::edge_colored_bounded_graph($this->BOUNDED_COMPLEX->MAXIMAL_POLYTOPES_COMBINATORIAL_DIMS,
$this->BOUNDED_COMPLEX->MAXIMAL_POLYTOPES,
$this->BOUNDED_COMPLEX->GRAPH);
}
weight 4.20;
rule BOUNDED_COMPLEX.GRAPH.EDGE_DIRECTIONS : BOUNDED_COMPLEX.GRAPH.ADJACENCY, BOUNDED_COMPLEX.VERTICES {
$this->BOUNDED_COMPLEX->GRAPH->EDGE_DIRECTIONS = edge_directions($this->BOUNDED_COMPLEX->GRAPH,$this->BOUNDED_COMPLEX->VERTICES);
}
rule BOUNDED_COMPLEX.GRAPH.EDGE_LENGTHS : BOUNDED_COMPLEX.GRAPH.EDGE_DIRECTIONS {
$this->BOUNDED_COMPLEX->GRAPH->EDGE_LENGTHS=[ map {
my $max=0;
assign_max($max, abs($_)) for @$_;
$max
} @{$this->BOUNDED_COMPLEX->GRAPH->EDGE_DIRECTIONS} ];
}
weight 3.10;
rule BOUNDED_COMPLEX.GRAPH.TOTAL_LENGTH : BOUNDED_COMPLEX.GRAPH.EDGE_LENGTHS {
my $l=0;
foreach (@{$this->BOUNDED_COMPLEX->GRAPH->EDGE_LENGTHS}) {
$l+=$_;
}
$this->BOUNDED_COMPLEX->GRAPH->TOTAL_LENGTH=$l;
}
weight 2.10;
rule BOUNDED_COMPLEX.DUAL_GRAPH.NODE_LABELS = FACET_LABELS;
rule BOUNDED_COMPLEX.GRAPH.NODE_LABELS = VERTEX_LABELS;
rule BOUNDED_COMPLEX.HASSE_DIAGRAM.ADJACENCY, BOUNDED_COMPLEX.HASSE_DIAGRAM.DECORATION, BOUNDED_COMPLEX.HASSE_DIAGRAM.INVERSE_RANK_MAP, \
BOUNDED_COMPLEX.HASSE_DIAGRAM.TOP_NODE, BOUNDED_COMPLEX.HASSE_DIAGRAM.BOTTOM_NODE : \
VERTICES_IN_FACETS, FAR_FACE, BOUNDED_COMPLEX.VERTEX_MAP {
$this->BOUNDED_COMPLEX->HASSE_DIAGRAM=relabeled_bounded_hasse_diagram($this->VERTICES_IN_FACETS, $this->FAR_FACE, $this->BOUNDED_COMPLEX->VERTEX_MAP);
}
precondition : FAR_FACE { $this->FAR_FACE->size()>0 };
weight 6.20;
rule BOUNDED_COMPLEX.MAXIMAL_POLYTOPES : HASSE_DIAGRAM.ADJACENCY, HASSE_DIAGRAM.DECORATION, HASSE_DIAGRAM.INVERSE_RANK_MAP, HASSE_DIAGRAM.TOP_NODE, HASSE_DIAGRAM.BOTTOM_NODE, FAR_FACE, BOUNDED_COMPLEX.VERTEX_MAP, N_VERTICES {
$this->BOUNDED_COMPLEX->MAXIMAL_POLYTOPES=bounded_complex($this->HASSE_DIAGRAM, $this->FAR_FACE, $this->BOUNDED_COMPLEX->VERTEX_MAP, $this->N_VERTICES);
}
precondition : FAR_FACE { $this->FAR_FACE->size()>0 };
rule BOUNDED_COMPLEX.VERTICES, BOUNDED_COMPLEX.MAXIMAL_POLYTOPES, BOUNDED_COMPLEX.VERTEX_MAP : VERTICES, VERTICES_IN_FACETS {
$this->BOUNDED_COMPLEX->MAXIMAL_POLYTOPES = $this->VERTICES_IN_FACETS;
$this->BOUNDED_COMPLEX->VERTICES = $this->VERTICES;
$this->BOUNDED_COMPLEX->VERTEX_MAP = new Array<Int>(sequence(0,$this->VERTICES->rows()));
}
precondition : FAR_FACE { $this->FAR_FACE->size()==0 };
weight 0.10;
rule BOUNDED_COMPLEX.VERTICES, BOUNDED_COMPLEX.VERTEX_MAP : VERTICES, FAR_FACE, N_VERTICES {
$this->BOUNDED_COMPLEX->VERTICES=$this->VERTICES->minor(~($this->FAR_FACE),All);
$this->BOUNDED_COMPLEX->VERTEX_MAP = new Array<Int>(sequence(0, $this->VERTICES->rows()) - $this->FAR_FACE);
}
precondition : POINTED;
weight 0.20;
rule BOUNDED_COMPLEX.VERTEX_MAP : BOUNDED_COMPLEX.VERTICES, VERTICES, FAR_FACE {
$this->BOUNDED_COMPLEX->VERTEX_MAP = find_bounded_mapping($this->BOUNDED_COMPLEX->VERTICES, $this->VERTICES, $this->FAR_FACE);
}
weight 2.1;
rule BOUNDED_COMPLEX.BOUNDED : {
$this->BOUNDED_COMPLEX->BOUNDED=1;
}
weight 0.1;
rule BOUNDED_COMPLEX.N_VERTICES = N_BOUNDED_VERTICES;
rule BOUNDED_COMPLEX.FAN_AMBIENT_DIM = CONE_AMBIENT_DIM;
# @category Unbounded polyhedra
# Graph of the bounded subcomplex.
user_method BOUNDED_GRAPH = BOUNDED_COMPLEX.GRAPH;
# @category Unbounded polyhedra
# Dual graph of the bounded subcomplex.
user_method BOUNDED_DUAL_GRAPH = BOUNDED_COMPLEX.DUAL_GRAPH;
# @category Unbounded polyhedra
# [[HASSE_DIAGRAM]] constrained to affine vertices
# Nodes representing the maximal inclusion-independent faces are connected to the top-node
# regardless of their dimension
user_method BOUNDED_HASSE_DIAGRAM = BOUNDED_COMPLEX.HASSE_DIAGRAM;
}
# Local Variables:
# mode: perl
# c-basic-offset:3
# End:
|
