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OrbitDistribution

calculate the orbit distribution of a LAVF object.

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

OrbitDistribution( obj)

Parameters

obj

-

a LAVF object.

Description

• 

Let L be a LAVF object and is Lie algebra (see IsLieAlgebra). Then OrbitDistribution method returns the orbit distribution of L.

• 

The returned orbit distribution of obj is a Distribution object. A Distribution object has access to various methods, see Overview of the Distribution object for more detail.

• 

The orbit distribution is the infinitesimal version of the group orbit.

• 

This method is associated with the LAVF object. For more detail, see Overview of the LAVF object.

Examples

withLieAlgebrasOfVectorFields:

Typesetting:-Settingsuserep=true:

Typesetting:-Suppressξx,y,z,ηx,y,z,zetax,y,z:

Build vector fields associated with 3-d spatial rotations...

RxVectorFieldzDy+yDz,space=x,y,z

Rxzy+yz

(1)

RyVectorFieldxDz+zDx,space=x,y,z

Ryzxxz

(2)

RzVectorFieldyDx+xDy,space=x,y,z

Rzyx+xy

(3)

We now construct a LAVF object for SO(3) that are generated by these rotation vector fields.

VVectorFieldξx,y,zDx+ηx,y,zDy+zetax,y,zDz,space=x,y,z

Vξx+ηy+ζz

(4)

LEliminationLAVFV,Rx,Ry,Rz

Lξx+ηy+ζz&whereξ=ηyζzx,ηx=ζyz+ηx,ηy=0,ηz=ζy,ζy,y=0,ζx=ζyy+ζx,ζz=0

(5)

Find the orbit distribution of L...

ODOrbitDistributionL

ODyxx+y,zxx+z

(6)

OD is a Distribution object which has access to various methods, for example,

DimensionOD

2

(7)

IntegralsOD

x2+y2+z2

(8)

GetAnnihilatorOD

dx+ydyx+zdzx

(9)

Compatibility

• 

The OrbitDistribution command was introduced in Maple 2020.

• 

For more information on Maple 2020 changes, see Updates in Maple 2020.

See Also

LieAlgebrasOfVectorFields (Package overview)

LAVF (Object overview)

Distribution (Object overview)

LieAlgebrasOfVectorFields[VectorField]

LieAlgebrasOfVectorFields[EliminationLAVF]