The Orbit( alpha, G ) command returns the orbit of the point alpha under the action of the permutation group G.

The returned value is an object that supports the following methods.

The Orbits( G ) command returns the set of all orbits of the permutation group G.

$\mathrm{with}\left(\mathrm{GroupTheory}\right)\:$

$G≔\mathrm{RubiksCubeGroup}\left(\right)$

$G≔\mathrm{<\; a\; permutation\; group\; on\; 48\; letters\; with\; 6\; generators\; >}$

$\mathrm{O1}≔\mathrm{Orbit}\left(1\&comma;G\right)$

$\mathrm{O1}≔1^{\mathrm{<\; a\; permutation\; group\; on\; 48\; letters\; with\; 6\; generators\; >}}$

$\mathrm{numelems}\left(\mathrm{O1}\right)$

$24$

$2\&in;\mathrm{O1}$

$\mathrm{false}$

$\mathrm{O2}≔\mathrm{Orbit}\left(2\&comma;G\right)$

$\mathrm{O2}≔2^{\mathrm{<\; a\; permutation\; group\; on\; 48\; letters\; with\; 6\; generators\; >}}$

$\mathrm{numelems}\left(\mathrm{O2}\right)$

$24$

$\mathrm{orbs}≔\mathrm{Orbits}\left(G\right)$

$\mathrm{orbs}≔\left[1^{\mathrm{<\; a\; permutation\; group\; on\; 48\; letters\; with\; 6\; generators\; >}}\&comma;2^{\mathrm{<\; a\; permutation\; group\; on\; 48\; letters\; with\; 6\; generators\; >}}\right]$

$\mathrm{nops}\left(\mathrm{orbs}\right)$

$2$

$\mathrm{Elements}\left(\mathrm{O2}\right)$

$\left\{2\&comma;4\&comma;5\&comma;7\&comma;10\&comma;12\&comma;13\&comma;15\&comma;18\&comma;20\&comma;21\&comma;23\&comma;26\&comma;28\&comma;29\&comma;31\&comma;34\&comma;36\&comma;37\&comma;39\&comma;42\&comma;44\&comma;45\&comma;47\right\}$

The GroupTheory[Orbit] and GroupTheory[Orbits] commands were introduced in Maple 17.

For more information on Maple 17 changes, see Updates in Maple 17.