VectorField Object as Derivation Operator - Maple Programming Help

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VectorField Object as Derivation Operator

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

X( f)

Parameters

X

-

a VectorField object

f

-

scalar expression, or Vector, Matrix, list or table of scalar expressions

Description

• 

A VectorField object X can act as derivation operator.

• 

A derivation is an operator X such that Xf+g=Xf+Xg and Xfg=fXg+Xfg

• 

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

• 

When a vector field 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 VectorField object. For more detail, see Overview of the VectorField object.

Examples

withLieAlgebrasOfVectorFields:

XVectorFieldxDx+yDy,space=x,y

Xxx+yy

(1)

 

Xx2

2x2

(2)

 

Xx,x2,x3

x,2x2,3x3

(3)

AMatrixx,y,x2,y2

Axyx2y2

(4)

 

XA

xy2x22y2

(5)

Compatibility

• 

The VectorField Object as Derivation Operator command was introduced in Maple 2020.

• 

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

See Also

VectorField (Object overview)

LieAlgebrasOfVectorFields[VectorField]

LieDerivative