#  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.
#-------------------------------------------------------------------------------



# @category Producing other objects
# Produces the Coxeter group of type //type//. 
# The Dynkin diagrams of the different types can be
# found in the description of the clients [[simple_roots_type_A|simple_roots_type_*]].
# @param String type the type of the Coxeter group
# @return group::GroupOfPolytope the Coxeter group of type //type// 
user_function coxeter_group {
    my $type = $_[0];
    if (length($type) < 2) {
        die "coxeter_group: Type needs single letter followed by rank.";
    }
    my @chars = split(//, $type);
    my $n = $chars[1];
    my $rings = new Set<Int>(0..$n-1);
    my $p = wythoff($type,$rings);
    return new group::GroupOfPolytope($p->GROUP);
}


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