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DChange

perform change of variables in a vector field or a one-form.

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

DChange (tr, obj, newVars, options)

dchange (tr, obj, newVars, options)

Parameters

tr

-

set of equations corresponding to the transformation from the old variables on the left-hand side of the equations to the new variables on the right-hand side.

obj

-

a VectorField or OneForm object

newVars

-

a list of new variable names

options

-

optional arguments that will be passed down to PDEtools[dchange] command

Description

• 

The DChange method performs changes of variables in a VectorField or OneForm object.

• 

This method returns a new VectorField or OneForm object living on the space specified by newVars.

• 

The name dchange is provided as an alias.

• 

This DChange method is based on the existing Maple function PDEtools[dchange].

• 

These methods are associated with the VectorField and OneForm objects. For more detail see Overview of the VectorField object, Overview of the OneForm object.

Examples

withLieAlgebrasOfVectorFields:

 

RVectorFieldy,x,x,y

Ryx+xy

(1)

 

Change variables to use polar coordinates (r,theta):

PDChangex=rcosθ,y=rsinθ,R,r,θ

Pcosθ2+sinθ2θ

(2)

 

We can further simplify this VectorField object, using the overloaded builtin simplify:

simplifyP

θ

(3)

These two vector fields are on different spaces.

GetSpaceR

x,y

(4)

GetSpaceP

r,θ

(5)

Compatibility

• 

The DChange command was introduced in Maple 2020.

• 

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

See Also

VectorField (Object overview)

OneForm (Object overview)

LieAlgebrasOfVectorFields[VectorField]

LieAlgebrasOfVectorFields[OneForm]

GetSpace

PDEtools[dchange]

VectorField Builtins