Spracherkennung für: .tst vermutete Sprache: Unknown {[0] [0] [0]} [Methode: Schwerpunktbildung, einfache Gewichte, sechs Dimensionen]
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#W rt-act.tst Groupoids Package Chris Wensley
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## Section 4.6
gap> gpd_infolevel_saved := InfoLevel( InfoGroupoids );;
gap> SetInfoLevel( InfoGroupoids, 0 );;
gap> m3 := FullTransformationMonoid( 3 );;
gap> rm3 := RightActionGroupoid( m3 );
groupoid with 5 pieces:
1: single piece groupoid with rays: < Group(
[ IdentityTransformation, Transformation( [ 1, 3, 2 ] ) ] ),
[ Transformation( [ 1, 1, 1 ] ), Transformation( [ 2, 2, 2 ] ),
Transformation( [ 3, 3, 3 ] ) ],
[ IdentityTransformation, Transformation( [ 2, 1 ] ),
Transformation( [ 3, 1, 2 ] ) ] >
2: single piece groupoid with rays: < Group( [ IdentityTransformation ] ),
[ Transformation( [ 1, 1, 2 ] ), Transformation( [ 1, 1 ] ),
Transformation( [ 2, 2, 1 ] ), Transformation( [ 2, 2 ] ),
Transformation( [ 3, 3, 1 ] ), Transformation( [ 3, 3, 2 ] ) ],
[ IdentityTransformation, Transformation( [ 1, 3, 2 ] ),
Transformation( [ 2, 1 ] ), Transformation( [ 2, 3, 1 ] ),
Transformation( [ 3, 1, 2 ] ), Transformation( [ 3, 2, 1 ] ) ] >
3: single piece groupoid with rays: < Group( [ IdentityTransformation ] ),
[ Transformation( [ 1, 2, 1 ] ), Transformation( [ 1, 3, 1 ] ),
Transformation( [ 2, 1, 2 ] ), Transformation( [ 2, 3, 2 ] ),
Transformation( [ 3, 1, 3 ] ), Transformation( [ 3, 2, 3 ] ) ],
[ IdentityTransformation, Transformation( [ 1, 3, 2 ] ),
Transformation( [ 2, 1 ] ), Transformation( [ 2, 3, 1 ] ),
Transformation( [ 3, 1, 2 ] ), Transformation( [ 3, 2, 1 ] ) ] >
4: single piece groupoid with rays: < Group( [ IdentityTransformation ] ),
[ Transformation( [ 1, 2, 2 ] ), Transformation( [ 1, 3, 3 ] ),
Transformation( [ 2, 1, 1 ] ), Transformation( [ 2, 3, 3 ] ),
Transformation( [ 3, 1, 1 ] ), Transformation( [ 3, 2, 2 ] ) ],
[ IdentityTransformation, Transformation( [ 1, 3, 2 ] ),
Transformation( [ 2, 1 ] ), Transformation( [ 2, 3, 1 ] ),
Transformation( [ 3, 1, 2 ] ), Transformation( [ 3, 2, 1 ] ) ] >
5: single piece groupoid with rays: < Group( [ IdentityTransformation ] ),
[ IdentityTransformation, Transformation( [ 1, 3, 2 ] ),
Transformation( [ 2, 1 ] ), Transformation( [ 2, 3, 1 ] ),
Transformation( [ 3, 1, 2 ] ), Transformation( [ 3, 2, 1 ] ) ],
[ IdentityTransformation, Transformation( [ 1, 3, 2 ] ),
Transformation( [ 2, 1 ] ), Transformation( [ 2, 3, 1 ] ),
Transformation( [ 3, 1, 2 ] ), Transformation( [ 3, 2, 1 ] ) ] >
gap> orm3 := ObjectList( rm3 );;
gap> Homset(rm3,orm3[1],orm3[2]);
fail
gap> Homset( rm3, orm3[2], orm3[3] );
<homset Transformation( [ 1, 1, 2 ] ) -> Transformation( [ 1, 1 ] )
with head group Group( [ IdentityTransformation ] )>
gap> Display( last );
<homset Transformation( [ 1, 1, 2 ] ) -> Transformation( [ 1, 1 ] )
with elements:
[Transformation( [ 1, 3, 2 ] ) : Transformation( [ 1, 1, 2 ] ) ->
Transformation( [ 1, 1 ] )]
gap> Homset( rm3, orm3[1], orm3[14] );
<homset Transformation( [ 1, 1, 1 ] ) -> Transformation( [ 2, 2, 2 ] )
with head group Group(
[ IdentityTransformation, Transformation( [ 3, 2, 1 ] ) ] )>
gap> Display( last );
<homset Transformation( [ 1, 1, 1 ] ) -> Transformation( [ 2, 2, 2 ] )
with elements:
[Transformation( [ 2, 1 ] ) : Transformation( [ 1, 1, 1 ] ) ->
Transformation( [ 2, 2, 2 ] )]
[Transformation( [ 2, 3, 1 ] ) : Transformation( [ 1, 1, 1 ] ) ->
Transformation( [ 2, 2, 2 ] )]
gap> SetInfoLevel( InfoGroupoids, gpd_infolevel_saved );;
