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Home : Support : Online Help : Mathematics : Differential Equations : Lie Symmetry Method : Commands for PDEs (and ODEs) : LieAlgebrasOfVectorFields : LAVF : LieAlgebrasOfVectorFields/LAVF/IsAbelian

Center

calculate the center of a LAVF object.

IsAbelian

check if a LAVF is abelian (commutative)

IsCommutative

a synonym for IsAbelian

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

Center( obj)

IsAbelian( obj)

IsCommutative( 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 the Center method returns the center of L (i.e. the elements in L that commute with all of L), as a LAVF object.

• 

The name Centre is provided as an alias.

• 

Let L be a LAVF object which is a Lie algebra. Then IsAbelian(L) returns true if Center(L) = L. False otherwise.

• 

The name IsCommutative is provided an alias.

• 

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)

Construct a LAVF for E(2).

LLAVFV,E2

Lξx+ηy&whereξy,y=0,ξx=0,ηx=ξy,ηy=0

(3)

IsLieAlgebraL

true

(4)

CtrCenterL

Ctrξx+ηy&whereξ=0,η=0

(5)

L and its centre are not the same, therefore L is not abelian.

AreSameL,Ctr

false

(6)

IsAbelianL

false

(7)

IsCommutativeL

false

(8)

Compatibility

• 

The Center, IsAbelian and IsCommutative 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

AreSame