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#############################################################################
##
#W tree.gd automgrp package Yevgen Muntyan
#W Dmytro Savchuk
##
#Y Copyright (C) 2003 - 2018 Yevgen Muntyan, Dmytro Savchuk
##
#############################################################################
##
#C IsActingOnTree
##
## This is a category to which all objects acting on a tree belong: tree
## homomorphisms and groups and semigroups acting on trees.
##
DeclareCategory("IsActingOnTree", IsObject);
#############################################################################
##
#A SphericalIndex (<obj>)
##
## Returns "spherical index" of the tree on which <obj> acts. It is returned
## as a tuple of two lists [start, period], where start may be empty.
##
DeclareAttribute("SphericalIndex", IsActingOnTree);
InstallSubsetMaintenance(SphericalIndex, IsCollection, IsCollection);
#############################################################################
##
#A TopDegreeOfTree (<obj>)
##
## Returns the degree of the tree on the first level, i.e. the number of vertices
## adjacent to the root vertex.
##
DeclareAttribute("TopDegreeOfTree", IsActingOnTree);
InstallSubsetMaintenance(TopDegreeOfTree, IsCollection, IsCollection);
#############################################################################
##
#O DegreeOfLevel (<obj>, <lev>)
##
## Returns degree of the tree on the level <lev>.
##
DeclareOperation("DegreeOfLevel", [IsActingOnTree, IsPosInt]);
#############################################################################
##
#P IsActingOnRegularTree (<obj>)
##
## Tells whether <obj> is acting on a "regular" tree.
##
DeclareProperty("IsActingOnRegularTree", IsActingOnTree);
InstallSubsetMaintenance(IsActingOnRegularTree, IsCollection, IsCollection);
#############################################################################
##
#P IsActingOnBinaryTree (<obj>)
##
## Tells whether <obj> is acting on a "binary" tree.
##
DeclareProperty("IsActingOnBinaryTree", IsActingOnTree);
InstallSubsetMaintenance(IsActingOnBinaryTree, IsCollection, IsCollection);
InstallTrueMethod(IsActingOnRegularTree, IsActingOnBinaryTree);
#############################################################################
##
#A DegreeOfTree (<obj>)
##
## This is a synonym for TopDegreeOfTree~("TopDegreeOfTree") for the case of
## a regular tree. It is an error to call this method for an object which acts
## on a non-regular tree.
##
DeclareAttribute("DegreeOfTree", IsActingOnTree);
InstallSubsetMaintenance(DegreeOfTree, IsCollection, IsCollection);
#############################################################################
##
#O FixesVertex (<obj>, <v>)
##
## Returns whether <obj> fixes the vertex <v>. The vertex <v> may be given as a list, or as
## a positive integer, in which case it denotes the <v>-th vertex at the first
## level.
##
DeclareOperation("FixesVertex", [IsActingOnTree, IsObject]);
#############################################################################
##
#O FixesLevel (<obj>, <lev>)
##
## Returns whether <obj> fixes level <lev>, i.e. fixes every vertex at the level
## <lev>.
##
DeclareOperation("FixesLevel", [IsActingOnTree, IsPosInt]);
#############################################################################
##
#A AbelImage(<obj>)
##
## Returns image of <obj> in the canonical projection onto the abelianization of
## the full group of tree automorphisms, represented as a subgroup of the additive
## group of rational functions.
##
DeclareAttribute("AbelImage", IsActingOnTree);
#XXX it doesn't make sense for non-invertible automata, does it?
#E
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