62.18 Elements for semigroups

Elements( sg )

Elements computes the elements of the semigroup sg. Note: the GAP standard library dispatcher function Elements calls the function sg.operations.Elements which performs a simple closure algorithm.

  gap> t1 := Transformation( [1..3], [1,1,2] );
  Transformation( [ 1, 2, 3 ], [ 1, 1, 2 ] )
  gap> t2 := Transformation( [1..3], [2,3,3] );
  Transformation( [ 1, 2, 3 ], [ 2, 3, 3 ] )
  gap> s := TransformationSemigroup( t1, t2 );
  TransformationSemigroup( Transformation( [ 1, 2, 3 ], 
  [ 1, 1, 2 ] ), Transformation( [ 1, 2, 3 ], [ 2, 3, 3 ] ) ) 
  gap> Elements( s );
  [ Transformation( [ 1, 2, 3 ], [ 1, 1, 1 ] ), 
    Transformation( [ 1, 2, 3 ], [ 1, 1, 2 ] ), 
    Transformation( [ 1, 2, 3 ], [ 1, 2, 2 ] ), 
    Transformation( [ 1, 2, 3 ], [ 2, 2, 2 ] ), 
    Transformation( [ 1, 2, 3 ], [ 2, 2, 3 ] ), 
    Transformation( [ 1, 2, 3 ], [ 2, 3, 3 ] ), 
    Transformation( [ 1, 2, 3 ], [ 3, 3, 3 ] ) ]

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