`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 ] ]Version 2.4 (May 1998)