IsTrivial - Maple Help
For the best experience, we recommend viewing online help using Google Chrome or Microsoft Edge.

Online Help

All Products    Maple    MapleSim


IsTrivial

check if the Killing form of a LAVF object is trivial.

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

IsTrivial( obj)

Parameters

obj

-

a KF object that is constructed by the method KillingForm.

Description

• 

Let K be the Killing form of a LAVF object L. Then IsTrivial(K) checks if the Killing form of L is trivial (i.e. KX,Y=0 for all vector fields X,Y solving L).

• 

This method is associated with the local KF object. For more detail, see Overview of the KF object for more detail.

Examples

withLieAlgebrasOfVectorFields:

Typesetting:-Settingsuserep=true:

Typesetting:-Suppressξx,y,ηx,y:

VVectorFieldξx,yDx+ηx,yDy,space=x,y

Vξⅆⅆx+ηⅆⅆy

(1)

E2LHPDE2y2ξx,y=0,xηx,y=yξx,y,yηx,y=0,xξx,y=0,indep=x,y,dep=ξ,η

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

(2)

We first construct a LAVF object for E(2).

LLAVFV,E2

Lξⅆⅆx+ηⅆⅆy&whereξy,y=0,ξx=0,ηx=ξy,ηy=0

(3)

IsLieAlgebraL

true

(4)

Get its KillingForm as a local KF object.

KKillingFormL

KX,Y→2yXxyYx

(5)

IsTrivialK

false

(6)

Compatibility

• 

The IsTrivial 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)

KF (Object overview)

LieAlgebrasOfVectorFields[VectorField]

LieAlgebrasOfVectorFields[LHPDE]

LieAlgebrasOfVectorFields[LAVF]

IsLieAlgebra

KillingForm