CycleLengths( g, D )
CycleLengths( g, D, operation )
CycleLengths
returns a list of the lengths of the cycles of the group
element g on the domain D, which must be a list of points of
arbitrary type. See Cycle for the definition of cycles.
It is allowed that D is a proper subset of a domain, i.e., that D is not invariant under the operation of g. In this case D is silently replaced by the smallest superset of D which is invariant.
The ordering of the lengths of cycles in the list returned by
CycleLengths
corresponds to the list of cycles returned by Cycles
,
which is ordered with respect to the smallest point in each cycle.
CycleLengths
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> CycleLengths( (1,5,3,8)(4,6,7), [3,5,7] ); [ 4, 3 ] gap> CycleLengths( (1,5,3,8)(4,6,7), [[1,3],[4,6]], OnPairs ); [ 4, 3 ]
CycleLengths
calls
Domain([g]).operations.CycleLengths( 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.CycleLengths
,
which takes elements from D, computes their orbit, removes all points
in the orbit from D, and repeats this until D has been emptied.
Special categories of group elements overlay this default function with
more efficient functions.
GAP 3.4.4