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GetChangeBasis

get the change of basis for an IDBasis object

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

GetChangeBasis( B, output = str)

GetChangeBasis( B, "newToOld")

Parameters

B

-

IDBasis object

str

-

(optional) a string: either "matrix" or "expression"

Description

• 

Let B be an IDBasis object associated with a LHPDE object S of finite type. The GetChangeBasis method returns the change-of-basis for initial data of S, as recorded in B.

• 

By default, the method returns a list of expressions which are linear combinations of the standard initial data basis (i.e. of the parametric derivatives from the associated LHPDE object S).

• 

The method can return the change-of-basis as a matrix by specifying the optional argument output = "matrix".

• 

In the second calling sequence, the call GetChangeBasis(B, "newToOld") returns the inverse of this change-of-basis matrix.

• 

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

Examples

withLieAlgebrasOfVectorFields:

Typesetting:-Settingsuserep=true:

Typesetting:-Suppressξx,y,ηx,y:

E2LHPDEdiffξx,y,y,y=0,diffηx,y,x=diffξx,y,y,diffηx,y,y=0,diffξx,y,x=0,indep=x,y,dep=ξ,η

E2ξy,y=0,ηx=ξy,ηy=0,ξx=0,indep=x,y,dep=ξ,η

(1)

The parametric derivatives of E2 are used as the standard initial data basis.

ParametricDerivativesE2

ξ,ξy,η

(2)

The IDBasis object B is constructed by specifying linear combinations of the standard initial data basis (i.e. of the parametric derivatives of E2).

BIDBasisE2,ξx,yydiffξx,y,y,ηx,yxdiffξx,y,y,diffξx,y,y

Bξyξy,ηxξy,ξy

(3)

GetChangeBasisB

ξyξy,ηxξy,ξy

(4)

The change-of-basis matrix and the standard basis elements.

GetChangeBasisB,output=matrix

1y00x10−10

(5)

GetParametricDerivativesB

ξ,ξy,η

(6)

The inverse matrix of the change-of-basis from B.

GetChangeBasisB,newToOld

10y00−101x

(7)

Compatibility

• 

The GetChangeBasis command was introduced in Maple 2020.

• 

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

See Also

IDBasis (Object overview)

LieAlgebrasOfVectorFields[IDBasis]

LieAlgebrasOfVectorFields[LHPDE]

ParametricDerivatives