#############################################################################
##
#W convertersfr.gd automgrp package Yevgen Muntyan
#W Dmytro Savchuk
##
#Y Copyright (C) 2003 - 2018 Yevgen Muntyan, Dmytro Savchuk
##
#############################################################################
##
#O FR2AutomGrp( <G> )
##
## This operation is designed to convert data structures defined in FR
## package written by Laurent Bartholdi to corresponding structures in
## AutomGrp package. Currently it is implemented for functionally recursive
## groups, semigroups, and their sub(semi)groups and elements.
##
## \beginexample
## gap> ZZ := FRGroup("t=<,t>[2,1]");
## <state-closed group over [ 1 .. 2 ] with 1 generator>
## gap> AZZ := FR2AutomGrp(ZZ);
## < t >
## gap> Display(AZZ);
## < t = (1, t)(1,2) >
## \endexample
## \beginexample
## gap> i4 := FRMonoid("s=(1,2)","f=<s,f>[1,1]");
## <state-closed monoid over [ 1 .. 2 ] with 2 generators>
## gap> Ai4 := FR2AutomGrp(i4);
## < 1, s, f >
## gap> Display(Ai4);
## < 1 = (1, 1),
## s = (1, 1)(1,2),
## f = (s, f)[1,1] >
## \endexample
## \beginexample
## gap> S := FRGroup("a=<a*b^-2,b^3>(1,2)","b=<b^-1*a,1>");
## <state-closed group over [ 1 .. 2 ] with 2 generators>
## gap> AS := FR2AutomGrp(S);
## < a, b >
## gap> Display(AS);
## < a = (a*b^-2, b^3)(1,2),
## b = (b^-1*a, 1) >
## gap> AssignGeneratorVariables(S);
## #I Assigned the global variables [ "a", "b" ]
## gap> x := a^3*b*a^-2;
## <2||a^3*b*a^-2>
## gap> DecompositionOfFRElement(x);
## [ [ <2||a*b^-2>, <2||b^3*a^2*b^-1*a^-1> ], [ 2, 1 ] ]
## gap> y := FR2AutomGrp(x);
## a^3*b*a^-2
## gap> Decompose(y);
## (a*b^-2, b^3*a^2*b^-1*a^-1)(1,2)
## \endexample
DeclareOperation("FR2AutomGrp", [IsObject]);
#############################################################################
##
#O AutomGrp2FR( <G> )
##
## This operation is designed to convert data structures defined in AutomGrp
## to corresponding structures in AutomGrp package written by Laurent
## Bartholdi. Currently it is implemented for automaton and self-similari
## (or, functionally recursive in L.Bartholdi's terminology) groups,
## semigroups, their sub(semi)groups and elements.
##
## \beginexample
## gap> G:=AutomatonGroup("a=(b,a)(1,2),b=(a,b)");
## < a, b >
## gap> FG := AutomGrp2FR(G);
## <state-closed group over [ 1 .. 2 ] with 2 generators>
## gap> DecompositionOfFRElement(FG.1);
## [ [ <2||b>, <2||a> ], [ 2, 1 ] ]
## gap> DecompositionOfFRElement(FG.2);
## [ [ <2||a>, <2||b> ], [ 1, 2 ] ]
## \endexample
## \beginexample
## gap> G := SelfSimilarGroup("a=(a*b^-2,b)(1,2),b=(b^2,a*b*a^-2)");
## < a, b >
## gap> F := AutomGrp2FR(G);
## <state-closed group over [ 1 .. 2 ] with 2 generators>
## gap> DecompositionOfFRElement(F.1);
## [ [ <2||a*b^-2>, <2||b> ], [ 2, 1 ] ]
## \endexample
## \beginexample
## gap> G := AutomatonGroup("a=(b,a)(1,2),b=(a,b),c=(c,a)(1,2)");
## < a, b, c >
## gap> H := Group([a*b,b*c^-2,a]);
## < a*b, b*c^-2, a >
## gap> FH := AutomGrp2FR(H);
## <recursive group over [ 1 .. 2 ] with 3 generators>
## gap> DecompositionOfFRElement(FH.1);
## [ [ <2||b^2>, <2||a^2> ], [ 2, 1 ] ]
## \endexample
## \beginexample
## gap> G := SelfSimilarSemigroup("a=(a*b^2,b*a)[1,1],b=(b,a*b*a)(1,2)");
## < a, b >
## gap> S := AutomGrp2FR(G);
## <state-closed semigroup over [ 1 .. 2 ] with 2 generators>
## gap> DecompositionOfFRElement(S.1);
## [ [ <2||a*b^2>, <2||b*a> ], [ 1, 1 ] ]
## \endexample
## \beginexample
## gap> G := AutomatonGroup("a=(b,a)(1,2),b=(a,b),c=(c,a)(1,2)");
## < a, b, c >
## gap> Decompose(a*b^-2);
## (b^-1, a^-1)(1,2)
## gap> x := AutomGrp2FR(a*b^-2);
## <2||a*b^-2>
## gap> DecompositionOfFRElement(x);
## [ [ <2||b^-1>, <2||a^-1> ], [ 2, 1 ] ]
## \endexample
##
DeclareOperation("AutomGrp2FR", [IsObject]);
#E
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