Some problems with IdempotentTester/Creater for transformation semigroups...

Issue #89 resolved
James Mitchell
repo owner created an issue

Something is wrong here...

gap> S:=Semigroup( [ Transformation( [ 2, 1, 3, 1, 4, 3 ] ), 
>  Transformation( [ 2, 2, 2, 2, 1, 2 ] ), Transformation( [ 5, 3, 4, 3, 5 ] ),
> Transformation( [ 6, 4, 1, 4, 5, 3 ] ), 
>  Transformation( [ 6, 5, 2, 6, 3, 4 ] ) ] );;
gap> NrIdempotents(S)=Number(HClasses(S), IsGroupHClass);
false

but

gap> gens:=ShallowCopy(last);
[ Transformation( [ 2, 1, 3, 1, 4, 3 ] ), 
  Transformation( [ 2, 2, 2, 2, 1, 2 ] ), Transformation( [ 5, 3, 4, 3, 5 ] ),
  Transformation( [ 6, 4, 1, 4, 5, 3 ] ), 
  Transformation( [ 6, 5, 2, 6, 3, 4 ] ) ]
gap> gens[3]:= Transformation( [ 5, 3, 4, 3, 5, 6 ] );
Transformation( [ 5, 3, 4, 3, 5 ] )
gap> INT_DEG_TRANS(gens[3]);
6
gap> List(gens, INT_DEG_TRANS);
[ 6, 6, 6, 6, 6 ]
gap> S:=Semigroup(gens);
<transformation semigroup on 6 pts with 5 generators>
gap> NrIdempotents(S); Number(HClasses(S), IsGroupHClass);
354
354

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