1.19 PartialOrderDClasses

PartialOrderDClasses( M )

The inclusion order on the set of the two sided principal ideals of the monoid M induces a natural order on the D classes of M. PartialOrderDClasses returns this partial order of the D classes of the monoid M as a binary relation.

    gap> M:= Monoid( Transformation( [ 2, 1, 2 ] ),
    > Transformation( [ 1, 2, 2 ] ) );;
    gap> PartialOrderDClasses(M);
    Relation( [ [ 1, 2 ], [ 2 ] ] ) 

The function HasseDiagram (see HasseDiagram) can be used to convert this binary relation into a smaller one that implies the same partial order.

   
[Index]