5.2 Orbit for Monoids

Orbit( M, d )
Orbit( M, d, action )

The orbit of a point d under the action of a monoid M is the set {d^m | m in M} of all points that are images of d under some element m in M.

In the first form Orbit computes the orbit of point d under the monoid M with respect to the canonical action OnPoints.

In the second form Orbit computes the orbit of point d under the monoid M with respect to the action action.

    gap> M:= Monoid( [ Transformation( [ 5, 4, 4, 2, 1 ] ), 
      Transformation( [ 2, 5, 5, 4, 1 ] ) ] ) ;
    gap> Orbit(M, 1); 
    [ 1, 5, 2, 4 ]
    gap> Orbit(M, 3, OnPoints);
    [ 3, 4, 5, 2, 1 ]
    gap> Orbit(M, [1,2], OnSets);
    [ [ 1, 2 ], [ 4, 5 ], [ 2, 5 ], [ 1, 4 ], [ 1, 5 ], [ 2, 4 ] ]
    gap> Orbit(M, [1,2], OnPairs);
    [ [ 1, 2 ], [ 5, 4 ], [ 2, 5 ], [ 1, 4 ], [ 4, 1 ], [ 5, 1 ], [ 5, 2 ], 
      [ 2, 4 ], [ 4, 2 ], [ 1, 5 ], [ 4, 5 ], [ 2, 1 ] ]

   
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