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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 SimplicialComplex {
# @category Topology
# A finite representation of the fundamental group.
# The fundamental group is represented as a pair of an integer,
# the number of generators, and a list of relations. The generators are numbered
# consecutively starting with zero. A relation is encoded as a list of pairs,
# each pair consisting of a generator and its exponent.
#
# You may use the [[fundamental2gap]] method to produce a ''GAP'' file.
property FUNDAMENTAL_GROUP : Pair<Int,List<List<Pair<Int,Int>>>>;
# @category Topology
# Labels of the generators of the [[FUNDAMENTAL_GROUP]].
# The labels can be chosen freely. If the [[FUNDAMENTAL_GROUP]] is computed
# by polymake, the generators correspond to the edges of the
# complex. Hence they are labeled ''g'' followed by the vertices of the edge, e.g.
# ''g3_6'' corresponds to the edge {3 6}.
property FUNDAMENTAL_GROUP_GEN_LABELS : Array<String>;
rule FUNDAMENTAL_GROUP, FUNDAMENTAL_GROUP_GEN_LABELS : FACETS, GRAPH.ADJACENCY {
fundamental_group($this);
}
precondition : GRAPH.CONNECTED;
# @category Topology
# Writes the [[FUNDAMENTAL_GROUP]] using [[FUNDAMENTAL_GROUP_GEN_LABELS]] to
# the given file in [[wiki:external_software#GAP|GAP]] input format.
# @param String filename
# @return String
user_method fundamental2gap(;$) {
my ($this, $gap_file)=@_;
$gap_file ||= $this->name . ".gap";
open my $out, ">", "$gap_file" or die "fundamental2gap: can't open $gap_file for writing";
my @gen_labels = split /\s+/, $this->FUNDAMENTAL_GROUP_GEN_LABELS;
my ($n_relations,$relations) = @{$this->FUNDAMENTAL_GROUP};
my @gap_relations;
foreach (@$relations) {
my @terms = map {
my ($gen_id,$exp) = @$_;
"$gen_labels[$gen_id]" . ( $exp==1 ? "" : "^$exp");
} @$_;
push @gap_relations, join("*", @terms);
}
foreach (@gen_labels) {
$_ = "\"$_\"";
}
print $out "F := FreeGroup(", join(", ",@gen_labels), ");\n";
print $out "AssignGeneratorVariables(F);\n";
print $out "G := F / [",join(", ",@gap_relations),"];\n";
print $out <<'.';
Print("FreeGroup is called F, after division by relators it's called G.\n");
Print("Use H:=SimplifiedFpGroup(G) to get a simplified representation H of the group G.\n");
.
close $out;
$gap_file; # as return value
}
}
# Local Variables:
# mode: perl
# cperl-indent-level:3
# indent-tabs-mode:nil
# End:
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