[MONOiD]

5.3 StrongOrbit

StrongOrbit( M, d, action )
StrongOrbit( M, d, action, grad )

The strong orbit of the point d in D under the action of M with respect to the grading grad is the set {d^{m_1} | m_1 in M, d^(m_1 m_2) = d mbox{ for some } m_2 in M}.

Note that the orbit of a point in general consists of several strong orbits.

In the first form StrongOrbit determines the strong orbit of point d under M with respect to the action action and the trivial grading.

In the second form StrongOrbit determines the strong orbit of point d under M with respect to the action action. Moreover, the grading grad is used to facilitate the calculations. Note, however, that the strong orbit of a point does not depend on the chosen grading.

    gap> M:= Monoid( [ Transformation( [ 5, 4, 4, 2, 1 ] ), 
    > Transformation( [ 2, 5, 5, 4, 1 ] ) ] ) ;
    gap> Orbit( M, 3 );
    [ 3, 4, 5, 2, 1 ]
    gap> StrongOrbit( M, 3, OnPoints );
    [ 3 ] 
Note that StrongOrbit always requires the argument action specifying how the monoid acts (see Other Actions).

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Version 2.4 (May 1998)

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