1##############################################################################
2##
3#W  example7.tst                 KBMag Package                      Derek Holt
4##
5gap> START_TEST( "KBMag package: example7.tst" );
6gap> fsa_infolevel_saved := InfoLevel( InfoFSA );;
7gap> SetInfoLevel( InfoFSA, 0 );;
8gap> rws_infolevel_saved := InfoLevel( InfoRWS );;
9gap> SetInfoLevel( InfoRWS, 0 );;
10
11gap> ## SubSection 1.15, Example 2
12gap> ## We find a free subgroup of the Fibonacci group F(2, 8).
13gap> ## This example may take about 20 minutes to run on a typical WorkStation.
14gap> F := FreeGroup( 8 );;
15gap> a:=F.1;; b:=F.2;; c:=F.3;; d:=F.4;; e:=F.5;; f:=F.6;; g:=F.7;; h:=F.8;;
16gap> G := F/[ a*b*c^-1, b*c*d^-1, c*d*e^-1, d*e*f^-1,
17>             e*f*g^-1, f*g*h^-1, g*h*a^-1, h*a*b^-1 ];;
18gap> R := KBMAGRewritingSystem( G );;
19gap> S := SubgroupOfKBMAGRewritingSystem( R, [a,e] );;
20gap> AutomaticStructureOnCosetsWithSubgroupPresentation( R, S );
21gap> P := PresentationOfSubgroupOfKBMAGRewritingSystem( R, S );
22<fp group on the generators [ f1, f3 ]>
23gap> RelatorsOfFpGroup( P );
24[]
25gap> Index( R, S );
26infinity
27
28gap> ## SetInfoLevel( InfoFSA, fsa_infolevel_saved );;
29gap> ## SetInfoLevel( InfoRWS, rws_infolevel_saved );;
30gap> STOP_TEST( "example7.tst", 10000 );
31