`Display( `

`M` )

`Display`

displays the Green class structure of the transformation monoid
`M`. Each D class is displayed as its index in the list of all D classes
followed by some information about its structure in parenthesis. A D
class displayed as

`[`

`a`.`b`.`d`]

is a regular D class with a Schaccent127utzenberger group of size `a`,
consisting of `b` L classes, or `d` R classes. A D class displayed as

`{`

`a`.`b`x`c`.`d`x`e`}

is a nonregular D class with a Schaccent127utzenberger group of size
`a`, consisting of *<b> x <c>* L classes (of which `c` have the same
kernel), or *<d> x <e>* R classes (of which `e` have the same
image).

gap> M:= Monoid( Transformation( [ 7, 7, 1, 1, 5, 6, 5, 5 ] ), > Transformation( [ 3, 8, 3, 7, 4, 6, 4, 5 ] ) );; gap> Size( M ); 27 gap> Display( M ); Rank 8: 1[1.1.1] Rank 6: 3{1.1x1.1x1} Rank 5: 6{1.1x1.1x1} Rank 4: 2{1.1x1.1x1} 8[2.1.1] Rank 3: 4{1.1x1.4x1} 5[1.3.4] Rank 2: 7[1.5.1]

The partial order of D classes (see PartialOrderDClasses) is determined in
terms of the indices that serve as names of D classes for `Display`

.

gap> HasseDiagram(PartialOrderDClasses(M)); Relation( [ [ 2, 3 ], [ 5 ], [ 6 ], [ 7 ], [ 4 ], [ 8 ], [ ], [ 5 ] ] )Version 2.4 (May 1998)