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# 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 {
rule FAR_FACE : VERTICES {
$this->FAR_FACE=far_points($this->VERTICES);
}
weight 1.10;
method has_far_facet {
my ($this)=@_;
my $Points=$this->give("VERTICES | POINTS");
rank($Points->minor(far_points($Points), range(1,$Points->cols-1))) == $this->CONE_DIM-1
}
# @category Unbounded polyhedra
# Indices of facets that are unbounded.
property UNBOUNDED_FACETS : Set;
# @notest Rule defined "in stock" - currently without use
rule UNBOUNDED_FACETS : FacetPerm.UNBOUNDED_FACETS, FacetPerm.PERMUTATION {
$this->UNBOUNDED_FACETS=permuted($this->FacetPerm->UNBOUNDED_FACETS, $this->FacetPerm->PERMUTATION);
}
weight 1.10;
rule UNBOUNDED_FACETS : VERTICES_IN_FACETS, FAR_FACE {
$this->UNBOUNDED_FACETS=incident_rows($this->VERTICES_IN_FACETS, $this->FAR_FACE);
}
# @category Unbounded polyhedra
# A linear objective function for which each unbounded edge is increasing;
# only defined for unbounded polyhedra.
property TOWARDS_FAR_FACE : Vector<Scalar>;
rule TOWARDS_FAR_FACE : VERTICES, AFFINE_HULL {
my $cone=new Polytope<Scalar>(INEQUALITIES => $this->VERTICES->minor($this->FAR_FACE,All),
EQUATIONS => $this->AFFINE_HULL);
$this->TOWARDS_FAR_FACE=$cone->REL_INT_POINT;
}
precondition : FAR_FACE { $this->FAR_FACE->size()>0 };
rule TOWARDS_FAR_FACE : { $this->TOWARDS_FAR_FACE=undef }
precondition : FAR_FACE { $this->FAR_FACE->size()==0 };
# @category Unbounded polyhedra
# True if each bounded vertex of a (possibly unbounded) d-polyhedron has vertex degree d in the [[GRAPH]].
# The vertex degrees of the vertices on the [[FAR_FACE]] do not matter.
property SIMPLE_POLYHEDRON : Bool;
rule SIMPLE, SIMPLE_POLYHEDRON : COMBINATORIAL_DIM, FAR_FACE, GRAPH.NODE_DEGREES {
my $simple=1;
my $simple_polyhedron=1;
my $v=0;
foreach (@{$this->GRAPH->NODE_DEGREES}) {
if ($_ != $this->COMBINATORIAL_DIM) {
$simple=0;
if (!exists($this->FAR_FACE->{$v})) {
$simple_polyhedron=0;
last;
}
}
++$v;
}
$this->SIMPLE=$simple;
$this->SIMPLE_POLYHEDRON=$simple_polyhedron;
}
weight 1.10;
rule SIMPLE_POLYHEDRON : { $this->SIMPLE_POLYHEDRON=1 }
precondition : SIMPLE;
weight 0.1;
# @category Unbounded polyhedra
# Number of bounded vertices (non-rays).
property N_BOUNDED_VERTICES : Int;
rule N_BOUNDED_VERTICES : N_VERTICES, FAR_FACE {
$this->N_BOUNDED_VERTICES=$this->N_VERTICES-@{$this->FAR_FACE};
}
weight 0.1;
# @category Unbounded polyhedra
# Indices of [[VERTICES]] that are no rays.
# @return Set<Int>
user_method BOUNDED_VERTICES : FAR_FACE, N_VERTICES {
my $this=shift;
range(0,$this->N_VERTICES-1) - $this->FAR_FACE;
}
# @category Unbounded polyhedra
# Indices of [[FACETS]] that are bounded.
# @return Set<Int>
user_method BOUNDED_FACETS : UNBOUNDED_FACETS, N_FACETS {
my $this=shift;
range(0,$this->N_FACETS-1) - $this->UNBOUNDED_FACETS;
}
}
object LinearProgram {
# Subgraph of [[BOUNDED_GRAPH]]. Consists only of directed arcs along which the value of the objective function increases.
property DIRECTED_BOUNDED_GRAPH : Graph<Directed>;
}
object Polytope {
rule LP.DIRECTED_BOUNDED_GRAPH.ADJACENCY : LP.DIRECTED_GRAPH.ADJACENCY, FAR_FACE, BOUNDED {
$this->LP->DIRECTED_BOUNDED_GRAPH->ADJACENCY= $this->BOUNDED ? $this->LP->DIRECTED_GRAPH->ADJACENCY : induced_subgraph($this->LP->DIRECTED_GRAPH->ADJACENCY, ~ $this->FAR_FACE);
}
weight 1.20;
}
# Local Variables:
# mode: perl
# cperl-indent-level:3
# indent-tabs-mode:nil
# End:
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