Cycle( g, d )
Cycle( g, d, operation )
Cycle
returns the orbit of the point d, which may be an object of
arbitrary type, under the group element g as a list of points.
The points e in the cycle of d under the group element g are those for which a power g^i exists such that d^{g^i} = e.
The first point in the list returned by Cycle
is the point d itself,
the ordering of the other points is such that each point is the image of
the previous point.
Cycle
accepts a function operation of two arguments d and g as
optional third argument, which specifies how the element g operates
(see Other Operations).
gap> Cycle( (1,5,3,8)(4,6,7), 3 ); [ 3, 8, 1, 5 ] gap> Cycle( (1,5,3,8)(4,6,7), [3,4], OnPairs ); [ [ 3, 4 ], [ 8, 6 ], [ 1, 7 ], [ 5, 4 ], [ 3, 6 ], [ 8, 7 ], [ 1, 4 ], [ 5, 6 ], [ 3, 7 ], [ 8, 4 ], [ 1, 6 ], [ 5, 7 ] ]
Cycle
calls
Domain([g]).operations.Cycle( g, d, operation )
and returns the value. Note that the third argument is not optional for
the functions called this way.
The default function called this way is GroupElementsOps.Cycle
, which
starts with d and applies g to the last point repeatedly until d is
reached again. Special categories of group elements overlay this default
function with more efficient functions.
GAP 3.4.4