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DerivedAlgebra

calculate the derived algebra of a LAVF object.

IsPerfect

check if a LAVF object is perfect.

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

DerivedAlgebra ( obj)

IsPerfect( obj)

Parameters

obj

-

a LAVF object that is a Lie algebra i.e. IsLieAlgebra(obj) returns true, see IsLieAlgebra.

Description

• 

Let L be a LAVF object which is a Lie algebra. Then DerivedAlgebra method returns the derived algebra L,L of L, as a LAVF object.

• 

Let L be a LAVF object and is Lie algebra. Then IsPerfect(L) returns true if and only if DerivedAlgebra(L) = L.

• 

These methods are 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)

IsLieAlgebraL

true

(4)

DLDerivedAlgebraL

DLξx+ηy&whereξx=0,ηx=0,ξy=0,ηy=0

(5)

Since L and DL are not the same, therefore L is not perfect.

IsPerfectL

false

(6)

Compatibility

• 

The DerivedAlgebra and IsPerfect commands were 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]

IsLieAlgebra