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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.
#-------------------------------------------------------------------------------
# @Category Combinatorics
object Polytope {
#rule PSEUDOVERTEX_LABELS : PSEUDOVERTEX_COVECTORS {
# $this->PSEUDOVERTEX_LABELS(temporary)=[ map { join("", @$_) } @{$this->PSEUDOVERTEX_COVECTORS} ];
#}
rule PROJECTIVE_AMBIENT_DIM : POINTS {
$this->PROJECTIVE_AMBIENT_DIM=$this->POINTS->cols-1;
}
weight 0.1;
rule PROJECTIVE_AMBIENT_DIM : DOME.VERTICES {
$this->PROJECTIVE_AMBIENT_DIM=$this->DOME->VERTICES->cols-2;
}
weight 0.1;
# checking feasibility via a tropical linear program
rule FEASIBLE, VALID_POINT : INEQUALITIES {
my $feasibility_pair = H_trop_input_feasible($this);
$this->VALID_POINT = $feasibility_pair->first;
$this->FEASIBLE = $feasibility_pair->second;
}
weight 3.1;
# A Polytope defined by a non-empty set of [[VERTICES]] or [[POINTS]] is always [[FEASIBLE]].
rule FEASIBLE, VALID_POINT : VERTICES | POINTS {
my $p=$this->give("VERTICES | POINTS");
if ($p->rows > 0) {
$this->VALID_POINT(temporary) = $p->row(0);
}
$this->FEASIBLE = $this->give("VERTICES | POINTS")->rows > 0;
}
weight 0.1;
rule VERTICES : INEQUALITIES {
$this->VERTICES = V_trop_input($this);
}
weight 6.10;
rule VERTICES, VERTICES_IN_POINTS : POINTS {
discard_non_vertices($this);
}
weight 1.20;
rule ENVELOPE.INEQUALITIES, ENVELOPE.EQUATIONS : POINTS {
$this->ENVELOPE = envelope($this->POINTS);
}
rule DOME.INEQUALITIES, DOME.FEASIBLE, DOME.BOUNDED : POINTS {
$this->DOME = dome_hyperplane_arrangement($this->POINTS);
}
rule DOME.MAXIMAL_COVECTOR_CELLS : DOME.VERTICES, DOME.VERTICES_IN_FACETS, DOME.FAR_FACE {
my $dome = $this->DOME;
my $V = $dome->VERTICES;
my $vif = new Set<Set<Int>>(rows($dome->VERTICES_IN_FACETS));
my $ff = $dome->FAR_FACE;
$dome->MAXIMAL_COVECTOR_CELLS = new IncidenceMatrix($vif - $ff);
}
rule PSEUDOVERTICES : DOME.VERTICES, DOME.FAR_FACE {
my $V = $this->DOME->VERTICES;
$this->PSEUDOVERTICES = $V->minor(~$this->DOME->FAR_FACE, ~scalar2set(0));
}
rule PSEUDOVERTEX_COVECTORS : PSEUDOVERTICES, POINTS {
$this->PSEUDOVERTEX_COVECTORS = covectors($this->PSEUDOVERTICES, $this->POINTS);
}
weight 1.10;
rule PSEUDOVERTEX_COARSE_COVECTORS : PSEUDOVERTICES, POINTS {
$this->PSEUDOVERTEX_COARSE_COVECTORS=coarse_covectors($this->PSEUDOVERTICES, $this->POINTS);
}
weight 1.10;
rule DOME.TROPICAL_POLYTOPE_VERTICES : DOME.VERTEX_COVECTORS {
my $pv = new Set();
for (my $i=0; $i < $this->DOME->VERTEX_COVECTORS->size; $i++) {
$pv += $i
if (0 == grep {$_->size==0} @{rows($this->DOME->VERTEX_COVECTORS->[$i])});
}
$this->DOME->TROPICAL_POLYTOPE_VERTICES = $pv;
}
rule TORUS_COVECTOR_DECOMPOSITION, MAXIMAL_COVECTORS : POINTS, DOME.VERTICES, DOME.VERTEX_COVECTORS, DOME.MAXIMAL_COVECTOR_CELLS, POLYTOPE_COVECTOR_DECOMPOSITION {
compute_covector_decomposition($this, compute_only_tropical_span=>0);
}
weight 6.10;
rule POLYTOPE_COVECTOR_DECOMPOSITION, DOME.TROPICAL_SPAN_MAXIMAL_COVECTOR_CELLS, POLYTOPE_MAXIMAL_COVECTORS : POINTS, DOME.VERTICES, DOME.VERTEX_COVECTORS, DOME.MAXIMAL_COVECTOR_CELLS {
compute_covector_decomposition($this, compute_only_tropical_span=>1);
}
weight 6.10;
rule MAXIMAL_COVECTORS : DOME.MAXIMAL_COVECTOR_CELLS, DOME.VERTICES, POINTS {
compute_maximal_covectors($this);
}
weight 2.10;
rule DOME.VERTEX_COVECTORS : DOME.VERTICES, POINTS {
$this->DOME->VERTEX_COVECTORS = covectors_of_scalar_vertices($this->DOME->VERTICES, $this->POINTS);
}
weight 1.10;
# In case [[VERTICES]] are known but [[POINTS]] are not, we set [[POINTS]] = [[VERTICES]].
# This allows to visualize a Polytope that was initialized via [[INEQUALIES]] with its coarsets [[POLYTOPE_COVECTOR_DECOMPOSITION]].
rule POINTS = VERTICES;
}
# Local Variables:
# mode: perl
# c-basic-offset:3
# End:
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