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GetVectorFields

get vector fields that form a basis for a Distribution object

GetAnnihilator

get one-forms that form a co-basis for a Distribution object

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

GetVectorFields( dist)

GetAnnihilator( dist)

Parameters

dist

-

a Distribution object.

Description

• 

The GetVectorFields method returns a list of VectorField objects which at each point form a basis of the subspace of tangent space associated with a distribution.  In the case where Distribution dist is in involution, the basis is chosen to commute.

• 

Similarly the GetAnnihilator method returns a list of OneForm objects which form a co-basis for the forms that annihilate the distribution.

• 

Both VectorField and OneForm objects are part of the LieAlgebrasOfVectorFields package. For more detail, see Overview of the LieAlgebrasOfVectorFields package.

• 

These methods are associated with the Distribution object. For more detail see Overview of the Distribution object.

Examples

withLieAlgebrasOfVectorFields:

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)

Construct the associated distribution...

ΣDistributionRx,Ry,Rz

Σyxx+y,zxx+z

(4)

GetVectorFieldsΣ

yxx+y,zxx+z

(5)

GetAnnihilatorΣ

dx+ydyx+zdzx

(6)

Compatibility

• 

The GetVectorFields and GetAnnihilator commands were introduced in Maple 2020.

• 

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

See Also

Distribution (Object overview)

LieAlgebrasOfVectorFields[Distribution]

VectorField (Object overview)

LieAlgebrasOfVectorFields[VectorField]

LieAlgebrasOfVectorFields (Package overview)