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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.
#-------------------------------------------------------------------------------
declare property_type SedentarityDecoration : c++ (name=>"fan::compactification::SedentarityDecoration", include=>"polymake/fan/compactification.h");
object PolyhedralComplex {
# @category Combinatorics
# The Hasse diagram of the compactification of the polyhedral complex.
#
# For a simplicial polyhedral complex, this is the cubical compactification
# (or cubical complex, see [Omid Amini: "The combinatorial Chow ring of
# products of graphs"]).
#
# For tropical varieties, this is the tropical compactification, as in
# [Brian Osserman and Joseph Rabinoff: "Lifting nonproper tropical
# intersections"].
#
# The vertices of the compactification correspond to the faces of the
# original complex that have the same dimension as their recession cone. We
# call the face corresponding to a vertex the 'realisation' of the vertex.
#
# The decoration has four entries:
# 1. The face in the vertices of the compactification
# 2. The rank of the face
# 3. The realisation of the face. This is the union of the realisations of
# the new vertices.
# 4. The sedentarity of the face. This is the intersection of the
# sedentarities of the vertices.
#
# @example [prefer cdd] The compactification of the positive orthant in three dimensions
# has the same Hasse diagram as the three dimensional cube.
# > $pc1 = new PolyhedralComplex(POINTS=>[[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]], INPUT_POLYTOPES=>[[0,1,2,3]]);
# > print $pc1->COMPACTIFICATION->DECORATION;
# | ({} 0 {} {})
# | ({0} 1 {0 1 2 3} {1 2 3})
# | ({1} 1 {0 2 3} {2 3})
# | ({2} 1 {0 1 3} {1 3})
# | ({3} 1 {0 1 2} {1 2})
# | ({4} 1 {0 3} {3})
# | ({5} 1 {0 2} {2})
# | ({6} 1 {0 1} {1})
# | ({7} 1 {0} {})
# | ({0 1} 2 {0 1 2 3} {2 3})
# | ({0 2} 2 {0 1 2 3} {1 3})
# | ({0 3} 2 {0 1 2 3} {1 2})
# | ({1 4} 2 {0 2 3} {3})
# | ({1 5} 2 {0 2 3} {2})
# | ({2 4} 2 {0 1 3} {3})
# | ({2 6} 2 {0 1 3} {1})
# | ({3 5} 2 {0 1 2} {2})
# | ({3 6} 2 {0 1 2} {1})
# | ({4 7} 2 {0 3} {})
# | ({5 7} 2 {0 2} {})
# | ({6 7} 2 {0 1} {})
# | ({0 1 2 4} 3 {0 1 2 3} {3})
# | ({0 1 3 5} 3 {0 1 2 3} {2})
# | ({0 2 3 6} 3 {0 1 2 3} {1})
# | ({1 4 5 7} 3 {0 2 3} {})
# | ({2 4 6 7} 3 {0 1 3} {})
# | ({3 5 6 7} 3 {0 1 2} {})
# | ({0 1 2 3 4 5 6 7} 4 {0 1 2 3} {})
# | ({-1} 5 {-1} {})
property COMPACTIFICATION : Lattice<SedentarityDecoration>;
rule COMPACTIFICATION.ADJACENCY, COMPACTIFICATION.DECORATION, \
COMPACTIFICATION.INVERSE_RANK_MAP, COMPACTIFICATION.TOP_NODE, \
COMPACTIFICATION.BOTTOM_NODE : \
FAR_VERTICES, VERTICES, HASSE_DIAGRAM.ADJACENCY, \
HASSE_DIAGRAM.DECORATION, HASSE_DIAGRAM.INVERSE_RANK_MAP, \
HASSE_DIAGRAM.TOP_NODE, HASSE_DIAGRAM.BOTTOM_NODE \
{
$this->COMPACTIFICATION = compactify($this);
}
}
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