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KillingPolynomial

calculate the Killing polynomial of a LAVF object.

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

KillingPolynomial( obj, lambda)

Parameters

obj

-

a LAVF object.

lambda

-

a variable name

Description

• 

Let L be a LAVF object. Then KillingPolynomial(L, 'lambda') returns the Killing polynomial (i.e. the characteristic polynomial of adjoint matrix) of L, as a function of lambda.

• 

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

Examples

withLieAlgebrasOfVectorFields:

Typesetting:-Settingsuserep=true:

Typesetting:-Suppressξx,y,ηx,y:

VVectorFieldξx,yDx+ηx,yDy,space=x,y

Vξx+ηy

(1)

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

(2)

Construct a vector fields system for E(2).

LLAVFV,E2

Lξx+ηy&whereξy,y=0,ξx=0,ηx=ξy,ηy=0

(3)

KillingPolynomialL,λ

λ3+ξy2λ

(4)

Compatibility

• 

The KillingPolynomial command was introduced in Maple 2020.

• 

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

See Also

LieAlgebrasOfVectorFields (Package overview)

LAVF (Object overview)

LieAlgebrasOfVectorFields[VectorField]

LieAlgebrasOfVectorFields[LHPDE]

LieAlgebrasOfVectorFields[LAVF]