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##############################################################################
##
#W logrws.tst Idrel Package Chris Wensley
#W & Anne Heyworth
#Y Copyright (C) 1999-2022 Anne Heyworth and Chris Wensley
##
gap> saved_infolevel_idrel := InfoLevel( InfoIdRel );;
gap> SetInfoLevel( InfoIdRel, 0 );;
## items defined in rws.tst
gap> F := FreeGroup( 2 );;
gap> f := F.1;; g := F.2;;
gap> relq8 := [ f^4, g^4, f*g*f*g^-1, f^2*g^2 ];;
gap> q8 := F/relq8;;
gap> SetName( q8, "q8" );;
gap> q8R := FreeRelatorGroup( q8 );;
gap> genq8R := GeneratorsOfGroup( q8R );;
gap> homq8R := FreeRelatorHomomorphism( q8 );;
gap> mq8 := MonoidPresentationFpGroup( q8 );;
gap> fmq8 := FreeGroupOfPresentation( mq8 );;
gap> id := One( fmq8 );;
gap> genfmq8 := GeneratorsOfGroup( fmq8 );;
gap> gprels := GroupRelatorsOfPresentation( mq8 );;
gap> invrels := InverseRelatorsOfPresentation( mq8 );;
gap> hompres := HomomorphismOfPresentation( mq8 );;
gap> q8labs := [ "a", "b", "A", "B" ];;
gap> SetMonoidPresentationLabels( q8, q8labs );;
gap> rws := RewritingSystemFpGroup( q8 );;
gap> T := F/[Comm(f,g)];;
gap> SetName( T, "T" );;
gap> SetArrangementOfMonoidGenerators( T, [1,-1,2,-2] );;
gap> Tlabs := [ "x", "X", "y", "Y" ];;
gap> mT := MonoidPresentationFpGroup( T );;
gap> fgmT := FreeGroupOfPresentation( mT );;
gap> genfgmT := GeneratorsOfGroup( fgmT );;
gap> SetMonoidPresentationLabels( T, Tlabs );;
gap> rwsT := RewritingSystemFpGroup( T );;
gap> r0 := InitialLoggedRulesOfPresentation( mq8 );;
gap> a := genfmq8[1];; b := genfmq8[2];;
gap> A := genfmq8[3];; B := genfmq8[4];;
gap> w0 := b^9 * a^-9;;
## Example 3.1.1
gap> r0 := InitialLoggedRulesOfPresentation( mq8 );;
gap> PrintLnUsingLabels( r0, genfmq8, q8labs );
[ [ a^-1, [ ], A ], [ b^-1, [ ], B ], [ A^-1, [ ], a ], [ B^-1,
[ ], b ], [ a*A, [ ], id ], [ b*B, [ ], id ], [ A*a, [ ], id ],
[ B*b, [ ], id ], [ a^4, [ [ 1, id ] ], id ], [ a^2*b^2, [ [ 4, id ] ], id ],
[ a*b*a*B, [ [ 3, id ] ], id ], [ b^4, [ [ 2, id ] ], id ] ]
## Example 3.1.2
gap> r1 := LoggedOnePassKB( mq8, r0 );;
gap> Length( r1 );
25
gap> PrintLnUsingLabels( r1, genfmq8, q8labs );
[ [ a^-1, [ ], A ], [ b^-1, [ ], B ], [ A^-1, [ ], a ], [ B^-1,
[ ], b ], [ a*A, [ ], id ], [ b*B, [ ], id ], [ A*a, [ ], id ],
[ B*b, [ ], id ], [ b^2, [ [ -4, id ], [ 2, A^2 ] ], a^2 ],
[ b^2, [ [ -1, id ], [ 4, A^2 ] ], a^2 ], [ a^3, [ [ 1, id ] ], A ],
[ a^3, [ [ 1, a ] ], A ], [ a^2*b, [ [ 4, id ] ], B ], [ a*b*a,
[ [ 3, id ] ], b ], [ a*b^2, [ [ 4, a ] ], A ], [ b*a*B, [
[ 3, a ] ], A ], [ b^3, [ [ 2, id ] ], B ], [ b^3, [ [ 2, b ] ], B ],
[ a*b^2, [ [ -1, id ], [ 4, A^3 ] ], a^3 ], [ b*a*B, [ [ -1, id ],
[ 3, A^3 ] ], a^3 ], [ b^3, [ [ -4, id ], [ 2, B*A^2 ] ], a^2*b ],
[ a^4, [ [ 1, id ] ], id ], [ a^2*b^2, [ [ 4, id ] ], id ],
[ a*b*a*B, [ [ 3, id ] ], id ], [ b^4, [ [ 2, id ] ], id ] ]
## Example 3.1.2
gap> r2 := LoggedRewriteReduce( mq8, r1 );;
gap> Length( r2 );
13
gap> PrintLnUsingLabels( r2, genfmq8, q8labs );
[ [ a^-1, [ ], A ], [ b^-1, [ ], B ], [ A^-1, [ ], a ], [ B^-1,
[ ], b ], [ a*A, [ ], id ], [ b*B, [ ], id ], [ A*a, [ ], id ],
[ B*b, [ ], id ], [ b^2, [ [ -4, id ], [ 2, A^2 ] ], a^2 ],
[ a^3, [ [ 1, id ] ], A ], [ a^2*b, [ [ 4, id ] ], B ], [ a*b*a,
[ [ 3, id ] ], b ], [ b*a*B, [ [ 3, a ] ], A ] ]
gap> r3 := LoggedKnuthBendix( mq8, r0 );;
gap> Length( r3 );
20
gap> PrintLnUsingLabels( r3, genfmq8, q8labs );
[ [ a^-1, [ ], A ], [ b^-1, [ ], B ], [ A^-1, [ ], a ], [ B^-1,
[ ], b ], [ a*A, [ ], id ], [ b*B, [ ], id ], [ A*a, [ ], id ],
[ B*b, [ ], id ], [ b*a, [ [ -3, id ], [ 4, B*A ] ], a*B ],
[ b^2, [ [ -4, id ], [ 2, A^2 ] ], a^2 ], [ b*A, [ [ -3, id ] ], a*b ],
[ A*b, [ [ -1, id ], [ 4, A ] ], a*B ], [ A^2, [ [ -1, id ] ], a^2 ],
[ A*B, [ [ -4, a ] ], a*b ], [ B*a, [ [ -4, id ], [ 3, A ] ], a*b ],
[ B*A, [ [ -3, a*b ] ], a*B ], [ B^2, [ [ -4, id ] ], a^2 ],
[ a^3, [ [ 1, id ] ], A ], [ a^2*b, [ [ 4, id ] ], B ], [ a^2*B,
[ [ -4, A^2 ], [ 1, id ] ], b ] ]
## Example 3.1.5
gap> lrws := LoggedRewritingSystemFpGroup( q8 );;
gap> PrintLnUsingLabels( lrws, genfmq8, q8labs );
[ [ a^-1, [ ], A ], [ b^-1, [ ], B ], [ A^-1, [ ], a ], [ B^-1,
[ ], b ], [ a*A, [ ], id ], [ b*B, [ ], id ], [ A*a, [ ], id ],
[ B*b, [ ], id ], [ b*a, [ [ -3, id ], [ 4, B*A ] ], a*B ],
[ b^2, [ [ -4, id ], [ 2, A^2 ] ], a^2 ], [ b*A, [ [ -3, id ] ], a*b ],
[ A*b, [ [ -1, id ], [ 4, A ] ], a*B ], [ A^2, [ [ -1, id ] ], a^2 ],
[ A*B, [ [ -4, a ] ], a*b ], [ B*a, [ [ -4, id ], [ 3, A ] ], a*b ],
[ B*A, [ [ -3, a*b ] ], a*B ], [ B^2, [ [ -4, id ] ], a^2 ],
[ a^3, [ [ 1, id ] ], A ], [ a^2*b, [ [ 4, id ] ], B ], [ a^2*B,
[ [ -4, A^2 ], [ 1, id ] ], b ] ]
gap> Length( lrws );
20
gap> lrwsT := LoggedRewritingSystemFpGroup( T );;
gap> PrintLnUsingLabels( lrwsT, genfgmT, Tlabs );
[ [ x^-1, [ ], X ], [ X^-1, [ ], x ], [ y^-1, [ ], Y ], [ Y^-1,
[ ], y ], [ x*X, [ ], id ], [ X*x, [ ], id ], [ y*Y, [ ], id ],
[ Y*y, [ ], id ], [ y*x, [ [ -1, X*Y ] ], x*y ], [ y*X, [ [ 1, Y ] ], X*y ],
[ Y*x, [ [ 1, X ] ], x*Y ], [ Y*X, [ [ -1, id ] ], X*Y ] ]
## Example 3.2.1
gap> PrintLnUsingLabels( w0, genfmq8, q8labs );
b^9*a^-9
gap> lw1 := LoggedOnePassReduceWord( w0, lrws );;
gap> PrintLnUsingLabels( lw1, genfmq8, q8labs );
[ [ [ -4, id ], [ 2, A^2 ], [ -3, b^-6*a^-2 ], [ 4, id ] ],
B*b^5*a*b*a^-8 ]
gap> lw2 := LoggedReduceWordKB( w0, lrws );;
gap> PrintLnUsingLabels( lw2, genfmq8, q8labs );
[ [ [ -4, id ], [ 2, A^2 ], [ -3, b^-6*a^-2 ], [ 4, id ], [ -3, b^-3 ],
[ 4, B*A*b^-3 ], [ -4, id ], [ 2, A^2 ], [ -3, B^-1*a^-1*b^-1*a^-2 ],
[ -4, a^-1*b^-1*a^-2 ], [ 3, A*a^-1*b^-1*a^-2 ], [ 4, id ],
[ -4, a^-2*B^-1 ], [ 2, A^2*a^-2*B^-1 ], [ -4, id ], [ 3, A ],
[ 1, b^-1*a^-1 ], [ -3, a^-1 ], [ -1, b^-1*a^-2 ], [ 4, id ],
[ -3, a*b ], [ -3, a*b*a^-1 ], [ -4, A^2 ], [ 1, id ], [ -3, id ] ], a*b ]
gap> SetInfoLevel( InfoIdRel, saved_infolevel_idrel );
#############################################################################
##
#E logrws.tst . . . . . . . . . . . . . . . . . . . . . . . . . . ends here
[ Dauer der Verarbeitung: 0.18 Sekunden
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