Wolfram Language & System 10.0 (2014)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

GroupOrbits

GroupOrbits[group,{p1,}]
returns the orbits of the points under the action of the elements of group.

GroupOrbits[group,{p1,},f]
finds the orbits under the group action given by a function f.

DetailsDetails

• Two points belong to the same orbit under group if there is an element g in group such that the image of one point under g is the other point.
• If a point p is fixed by all elements in group then it forms an orbit {p}.
• GroupOrbits[group] gives all orbits in the natural domain of action of group.
• Orbits are given as sorted lists.
• Evaluation of for an action function f, a point p and a permutation g of the given group, is assumed to return another point p'.
• For permutation groups, the default group action is taken to be PermutationReplace.

ExamplesExamplesopen allclose all

Basic Examples  (1)Basic Examples  (1)

Take a permutation group:

Orbit of point 3:

 Out[2]=

Point 7 belongs to the same orbit:

 Out[3]=

Point 4 belongs to a different orbit:

 Out[4]=