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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 Symmetry
# A symmetric polytope defined as the convex hull of the orbit of a single point
# under a permutation group acting on coordinates.
# currently only for [[Polytope<Rational>]]
declare object_specialization PointOrbit = Polytope<Rational> {
precondition : GROUP.COORDINATE_ACTION.N_POINTS_GENERATORS {
$this->GROUP->COORDINATE_ACTION->N_POINTS_GENERATORS==1;
}
#------------------------------------------------------
# properties
#------------------------------------------------------
property GROUP {
property COORDINATE_ACTION {
# The NOP-graph of [[POINTS_GENERATORS]] with respect to the
# [[GROUP]]. The nodes of the NOP-graph
# correspond to the [[REPRESENTATIVE_CERTIFIERS]],
# which represent the different orbit polytopes
# contained in the given orbit polytope.
property NOP_GRAPH : Graph<Directed>;
# A matrix of representatives of all certifiers
# for [[POINTS_GENERATORS]] with respect to the
# [[GROUP]].
# A certifier is an integer point in the
# given orbit polytope.
# Note that the representative certifiers must be in
# the same order as the corresponding nodes
# in the [[NOP_GRAPH]]. Further, the [[CP_INDICES]]
# refer to row indices of this property.
property REPRESENTATIVE_CERTIFIERS : Matrix<Rational>;
# The number of [[REPRESENTATIVE_CERTIFIERS]].
property N_REPRESENTATIVE_CERTIFIERS : Int;
# The row indices of all core points among
# the [[REPRESENTATIVE_CERTIFIERS]].
property CP_INDICES : Set<Int>;
# A matrix of representatives of all core points in
# the given orbit polytope.
# A core point is an integer point whose orbit
# polytope is lattice-free (i.e. does not contain
# integer points besides its vertices).
property REPRESENTATIVE_CORE_POINTS : Matrix<Rational>;
# The number of [[REPRESENTATIVE_CORE_POINTS]].
property N_REPRESENTATIVE_CORE_POINTS : Int;
}
}
#------------------------------------------------------
# rules
#------------------------------------------------------
rule GROUP.COORDINATE_ACTION.N_REPRESENTATIVE_CERTIFIERS : GROUP.COORDINATE_ACTION.REPRESENTATIVE_CERTIFIERS {
$this->GROUP->COORDINATE_ACTION->N_REPRESENTATIVE_CERTIFIERS = $this->GROUP->COORDINATE_ACTION->REPRESENTATIVE_CERTIFIERS->rows;
}
rule GROUP.COORDINATE_ACTION.N_REPRESENTATIVE_CORE_POINTS : GROUP.COORDINATE_ACTION.REPRESENTATIVE_CORE_POINTS {
$this->GROUP->COORDINATE_ACTION->N_REPRESENTATIVE_CORE_POINTS = $this->GROUP->COORDINATE_ACTION->REPRESENTATIVE_CORE_POINTS->rows;
}
rule GROUP.COORDINATE_ACTION.NOP_GRAPH, GROUP.COORDINATE_ACTION.REPRESENTATIVE_CERTIFIERS, GROUP.COORDINATE_ACTION.REPRESENTATIVE_CORE_POINTS, GROUP.COORDINATE_ACTION.CP_INDICES : GROUP.COORDINATE_ACTION.POINTS_GENERATORS, POINTS, LATTICE_POINTS_GENERATORS {
my @res=nestedOPGraph($this->GROUP->COORDINATE_ACTION->POINTS_GENERATORS->[0], $this->POINTS, $this->LATTICE_POINTS_GENERATORS->[0], $this->GROUP->COORDINATE_ACTION, 0);
$this->GROUP->COORDINATE_ACTION->NOP_GRAPH = $res[0];
$this->GROUP->COORDINATE_ACTION->REPRESENTATIVE_CERTIFIERS = $res[1];
$this->GROUP->COORDINATE_ACTION->REPRESENTATIVE_CORE_POINTS = $res[3];
$this->GROUP->COORDINATE_ACTION->CP_INDICES = $res[4];
}
precondition : BOUNDED;
precondition : FEASIBLE;
}
package Visual::Color;
# Color for the visualization of core points
custom $CorePointColor="236 101 0"; #tud8b
# Color for the visualization of non core points
custom $NonCorePointColor="0 131 204"; #tud2b
# Local Variables:
# mode: perl
# cperl-indent-level: 3
# indent-tabs-mode:nil
# End:
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