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OneForm Object as Operator

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

omega( X)

Parameters

omega

-

a OneForm object

X

-

a VectorField object

Description

• 

A OneForm object omega can act as an operator on a VectorField X, by contraction.

• 

if ω is a 1-form. and if X=i=1nξi is a vector field (both on a space with coordinates x1,x2,,xn), then their contraction is ωX=i=1nθiξi.

• 

Because it can act as an operator, a OneForm object is of type appliable. See Overview of OneForm Overloaded Builtins for more detail.

• 

When a OneForm is acting as an operator, it will distribute itself over indexable types such as Vectors, Matrices, lists, and tables.

• 

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

Examples

withLieAlgebrasOfVectorFields:

RxVectorFieldyDzzDy,space=x,y,z

Rxzy+yz

(1)

RyVectorFieldxDz+zDx,space=x,y,z

Ryzxxz

(2)

RzVectorFieldxDyyDx,space=x,y,z

Rzyx+xy

(3)

 

ωOneFormxdx+ydy+zdz,space=x,y,z

ωxdx+ydy+zdz

(4)

ωRx

0

(5)

ωRx,Ry,Rz

0,0,0

(6)

ωR

tablex=0,z=0,y=0

(7)

See Also

OneForm (Object overview)

LieAlgebrasOfVectorFields[OneForm]

LieAlgebrasOfVectorFields[VectorField]