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# Copyright (c) 1997-2015
# Ewgenij Gawrilow, Michael Joswig (Technische Universitaet Berlin, Germany)
# http://www.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 Group {
# Some generating set for the group. All generators must have
# the same length [[DEGREE]].
# FIXME: Concrete description as second row of permutation representation
property GENERATORS : Array< Array<Int> >;
rule initial : GENERATORS {
my $g=$this->GENERATORS;
my $length=$g->size && $g->[0]->size;
foreach (@$g) {
if ($_->size != $length) {
croak( "all generators must have the same length" );
}
my %vals;
foreach my $entry (@$_) {
if ($entry<0 || $entry>=$length) {
croak( "each generator must be a permutation of (0,...,DEGREE-1)" );
}
$vals{$entry}++;
}
if (keys %vals != $length) {
croak( "each generator must be a permutation of (0,...,DEGREE-1)" );
}
}
}
# Strong generating set with respect to [[BASE]].
property STRONG_GENERATORS : Array< Array<Int> >;
# The number of [[STRONG_GENERATORS]].
property N_STRONG_GENERATORS : Int;
# A base for [[STRONG_GENERATORS]].
property BASE : Array<Int>;
# The __degree__ of the permutation representation.
property DEGREE : Int;
# The __order__ of the group.
property ORDER : Integer;
# Transversals along the stabilizer chain.
property TRANSVERSALS : Array < Array<Int> >;
# The number of group elements per transversal.
property TRANSVERSAL_SIZES : Array<Int>;
# The character table.
# NOTE: We do not support complex characters, but for the moment only real rational ones.
property CHARACTER_TABLE : Matrix<Rational>;
# A set of representatives for each conjugacy class
property CONJUGACY_CLASS_REPRESENTATIVES : Array<Array<Int>>;
# The conjugacy classes themselves
property CONJUGACY_CLASSES : Array<Set<Array<Int>>>;
# The sizes of the conjugacy classes
property CONJUGACY_CLASS_SIZES : Array<Int>;
}
# Local Variables:
# mode: perl
# cperl-indent-level:3
# indent-tabs-mode:nil
# End:
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