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# Copyright (c) 1997-2018
# 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 {
# @category Symmetry
# The number of elements in the group
property ORDER : Integer;
# @category Symmetry
# The character table.
# NOTE: We do not support complex characters, but for the moment only real ones.
property CHARACTER_TABLE : Matrix<QuadraticExtension<Rational>>;
# @category Symmetry
# The sizes of the conjugacy classes
property CONJUGACY_CLASS_SIZES : Array<Int>;
#
# after these general properties,
# different actions that express representations of the group on different entities
#
# @category Symmetry
# a permutation action on integers
property PERMUTATION_ACTION : PermutationAction : multiple;
# @category Symmetry
# a permutation action on a collection of sets of integers
property SET_ACTION : PermutationAction<Set<Int>> : multiple;
# @category Symmetry
# an action on sets where only one representative for each orbit is stored
property IMPLICIT_SET_ACTION : ImplicitActionOnSets : multiple;
# @category Symmetry
# operates on indices
property INPUT_RAYS_ACTION : PermutationAction;
# @category Symmetry
# operates on indices
property RAYS_ACTION : PermutationAction;
# @category Symmetry
# operates on indices
property INEQUALITIES_ACTION : PermutationAction;
# @category Symmetry
# operates on indices
property FACETS_ACTION : PermutationAction;
# @category Symmetry
# operates on indices
property MAXIMAL_CONES_ACTION : PermutationAction;
# @category Symmetry
# operates on indices
property INPUT_CONES_ACTION : group::PermutationAction;
# @category Symmetry
# operates on indices
property FACET_NORMALS_ACTION : PermutationAction;
# @category Symmetry
# operates on indices, including the '0'-th homogeneous coordinate
property HOMOGENEOUS_COORDINATE_ACTION : PermutationAction;
# @category Symmetry
# operates on indices
property VECTOR_ACTION : PermutationAction;
# @category Symmetry
property REGULAR_REPRESENTATION : MatrixActionOnVectors<Rational>;
}
# Local Variables:
# mode: perl
# cperl-indent-level:3
# indent-tabs-mode:nil
# End:
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