`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.