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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.
#-------------------------------------------------------------------------------
# Polytope propagation means to define a polytope inductively by assigning vectors to arcs
# of a directed graph. At each node of such a graph a polytope arises as the joint convex hull
# of the polytopes at the translated sources of the inward pointing arcs.
#
# For details see
# Joswig: Polytope Propagation on Graphs.
# Chapter 6 in Pachter/Sturmfels: Algebraic Statistics for Computational Biology, Cambridge 2005.
#
# @example
# We define an acyclic digraph on 8 nodes with a unique source and a unique sink.
# Each arc is equipped with a vector in Q^2.
# > $Gamma = new GraphAdjacency<Directed>(8);
# > $Vectors = new EdgeMap<Directed, Vector>($Gamma);
# > $Vectors->edge(0,1) = [1,0]; $Vectors->edge(0,2) = [0,0];
# > $Vectors->edge(1,3) = [1,0]; $Vectors->edge(1,4) = [0,1];
# > $Vectors->edge(2,3) = [0,0]; $Vectors->edge(2,4) = [0,2];
# > $Vectors->edge(3,5) = [1,0]; $Vectors->edge(3,6) = [0,1];
# > $Vectors->edge(4,5) = [0,0]; $Vectors->edge(4,6) = [0,2];
# > $Vectors->edge(5,7) = [0,0];
# > $Vectors->edge(6,7) = [0,0];
# Then we can define the propagated polytope implicitly:
# > $P = new PropagatedPolytope(CONE_AMBIENT_DIM=>3, "SUM_PRODUCT_GRAPH.ADJACENCY"=>$Gamma, "SUM_PRODUCT_GRAPH.TRANSLATIONS"=>$Vectors);
# > print $P->VERTICES;
# | 1 3 0
# | 1 1 0
# | 1 0 1
# | 1 1 3
# | 1 0 4
# Note that it is necessary to specify the dimension of the (homogeneous) ambient space by setting [[CONE_AMBIENT_DIM]].
declare object PropagatedPolytope<Scalar=Rational> : Polytope<Scalar> {
# Directed graph to define the propagated polytope. There is a (translation) vector assigned to each arc.
# We assume that this graph is acyclic with a unique sink.
property SUM_PRODUCT_GRAPH : Graph<Directed> {
# The translation vectors of the arcs.
property TRANSLATIONS : EdgeMap<Directed,Vector<Scalar>> : construct(ADJACENCY);
}
rule VERTICES, VERTEX_NORMALS, LINEALITY_SPACE : SUM_PRODUCT_GRAPH, CONE_AMBIENT_DIM {
sum_product($this);
}
incurs VertexPerm;
}
# Local Variables:
# mode: perl
# cperl-indent-level:3
# indent-tabs-mode:nil
# End:
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