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#############################################################################
##
#W selfsim.gd automgrp package Yevgen Muntyan
#W Dmytro Savchuk
##
#Y Copyright (C) 2003 - 2018 Yevgen Muntyan, Dmytro Savchuk
##
###############################################################################
##
#C IsSelfSim
##
## A category of objects created using `SelfSimGroup'~("SelfSimGroup"). These
## objects are (possibly infinite) initial automata.
##
DeclareCategory("IsSelfSim", IsTreeHomomorphism);
DeclareCategoryCollections("IsSelfSim");
DeclareCategoryFamily("IsSelfSim");
InstallTrueMethod(IsActingOnRegularTree, IsSelfSimCollection);
InstallTrueMethod(IsActingOnRegularTree, IsSelfSim);
DeclareCategory("IsInvertibleSelfSim", IsSelfSim and IsTreeAutomorphism);
DeclareCategoryCollections("IsInvertibleSelfSim");
###############################################################################
##
#O SelfSim( <word>, <a> )
#O SelfSim( <word>, <fam> )
##
## Given assosiative word <word> constructs a tree homomorphism from the family
## <fam>, or to which homomorphism <a> belongs. This function is useful when
## one needs to make some operations with associative words. See also `Word' ("Word").
## \beginexample
## gap> G := SelfSimilarGroup("a=(a*b,b)(1,2), b=(a^-1,b)");
## < a, b >
## gap> F := UnderlyingFreeGroup(G);
## <free group on the generators [ a, b ]>
## gap> c := SelfSim(F.1*F.2^2,a);
## a*b^2
## gap> IsSelfSim(c);
## true
## \endexample
##
DeclareOperation("SelfSim", [IsAssocWord, IsSelfSim]);
DeclareOperation("SelfSim", [IsAssocWord, IsSelfSimFamily]);
DeclareOperation("SelfSim", [IsAssocWord, IsList]);
###############################################################################
##
#O StatesWords( <a> )
##
DeclareOperation("StatesWords", [IsSelfSim]);
###############################################################################
##
#P IsFiniteState( <a> )
##
## Returns `true' if <a> has finitely many different sections.
## It will never stop if the free reduction of words is not sufficient
## to establish the finite-state property or if <a> is not finite-state (has
## infinitely many different sections).
##
## See also `AllSections' ("AllSections") for the list of all sections and
## `MealyAutomaton' ("MealyAutomaton"), which allows to construct
## a Mealy automaton whose states are the sections of <a> and which
## encodes its action on the tree.
## \beginexample
## gap> D := SelfSimilarGroup("x=(1,y)(1,2), y=(z^-1,1)(1,2), z=(1,x*y)");
## < x, y, z >
## gap> IsFiniteState(x*y^-1);
## true
## \endexample
##
DeclareProperty("IsFiniteState", IsSelfSim);
DeclareOperation("OrderUsingSections",[IsSelfSim]);
DeclareOperation("OrderUsingSections",[IsSelfSim, IsCyclotomic]);
DeclareGlobalFunction("__AG_CreateSelfSim");
#E
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