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LieAlgebrasOfVectorFields

  

Differential

  

construct the differential of an expression

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

Differential( f, space = vars)

Parameters

f

-

a scalar expression, or a list, set or rtable of scalar expressions

vars

-

(optional) list of names giving the coordinates of the space

Description

• 

The differential command computes the differential of an algebraic expression, and returns a OneForm object

• 

The differential of a function f on a space with coordinates x1,x2,,xn is df=i=1n xifx1,..,xn dxi. See differential.

• 

The space on which f lives can be specified using the space= option. It may be necessary to specify this option if the expression f contains names that are not coordinates, or if f is independent of a name that is a coordinate.

• 

The Differential command maps itself over indexed structures such as lists and vectors.

• 

This command is part of the LieAlgebrasOfVectorFields package. It can be called using the form Differential(...) after executing the command with(LieAlgebrasOfVectorFields). It can also be directly called using the form :-LieAlgebrasOfVectorFields[Differential](...). The Differential command returns a OneForm object.  For more detail see Overview of the OneForm object.

Examples

withLieAlgebrasOfVectorFields:

 

Differentialfx,y

xfx,ydx+yfx,ydy

(1)

 

Differentiala2y2,space=x,y

2a2ydy

(2)

 

Differentialx2,y2,2xy,space=x,y

2xdx,2ydy,2ydx+2xdy

(3)

Compatibility

• 

The LieAlgebrasOfVectorFields[Differential] command was introduced in Maple 2020.

• 

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

See Also

OneForm (Object overview)

LieAlgebrasOfVectorFields (Package overview)