5.4 GradedOrbit

GradedOrbit( M, d, action, grad )

The graded orbit of the point d in D under the action of M with respect to the grading grad is the list [O_1, O_2, ... ] of sets O_i = {d^m | m in M, <grad>(d^m) = i}. Thus the orbit of d is simply the union of the sets O_i.

The function GradedOrbit determines the graded orbit of point d under M with respect to the grading grad and the action action.

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

Note that GradedOrbit always requires the argument action specifying how the monoid acts (see Other Actions).

   
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