5.5 ShortOrbit

ShortOrbit( M, d, action, grad )

The short orbit of the point d in D under the action of M with respect to the grading grad is the set {d^m | m in M, <grad>(d^m) = <grad>(d)}.

The function ShortOrbit determines the short orbit of the 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> ShortOrbit(M, [1, 2, 3], OnSets, Size);
   [ [ 1, 2, 3 ] ]

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

   
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