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GroupTheory

  

Orbit

  

compute the orbit of a point under the action of a permutation group

  

Orbits

  

compute all the orbits of a permutation group

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

Orbit( alpha, G )

Orbits( G )

Parameters

G

-

a permutation group

alpha

-

posint; a point whose orbit is to be computed

Description

• 

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.

Representative( orb )

returns a representative of the orbit orb

numelems( orb )

returns the cardinality of the orbit orb

member( x, orb ) or x in orb

returns true if x belongs to the orbit orb

Elements( orb )

returns the elements of the orbit orb, as a set

• 

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

Examples

withGroupTheory:

GRubiksCubeGroup

G < a permutation group on 48 letters with 6 generators >

(1)

O1Orbit1&comma;G

O11 < a permutation group on 48 letters with 6 generators >

(2)

numelemsO1

24

(3)

2inO1

false

(4)

O2Orbit2&comma;G

O22 < a permutation group on 48 letters with 6 generators >

(5)

numelemsO2

24

(6)

orbsOrbitsG

orbs1 < a permutation group on 48 letters with 6 generators > &comma;2 < a permutation group on 48 letters with 6 generators >

(7)

nopsorbs

2

(8)

ElementsO2

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

(9)

Compatibility

• 

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

• 

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

See Also

GroupTheory

GroupTheory[Elements]

GroupTheory[RubiksCubeGroup]

numelems

Perm