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IsLieAlgebra

check if a LAVF object is a Lie algebra

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

IsLieAlgebra( obj)

Parameters

obj

-

a LAVF object.

Description

• 

The method IsLieAlgebra checks if a LAVF object is a Lie algebra. In other words, let L be a LAVF object, then the method returns true if L,LL, false otherwise.

• 

IsLieAlgebra(L) is equivalent to AreCommuting(L,L,L). See AreCommuting for more detail.

• 

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)

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

LLAVFV,E2

Lξx+ηy&whereξy,y=0,ξx=0,ηx=ξy,ηy=0

(3)

These vector fields in fact form a Lie algebra.

IsLieAlgebraL

true

(4)

Compatibility

• 

The IsLieAlgebra 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]

AreCommuting