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IsInvariant

check if one LAVF is invariant under action of another LAVF

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

IsInvariant( L1, L2)

Parameters

L1, L2

-

LAVF objects.

Description

• 

Let L1, L2 be LAVF objects on the same space. Then IsInvariant(L1,L2) checks if L1 is invariant under action of L2 (i.e. if L1,L2L1).

• 

The call IsInvariant(L1, L2) is equivalent to the call AreCommuting(L1,L2,L1). 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)

T2LHPDEdiffξx,y,x=0,diffξx,y,y=0,diffηx,y,x=0,diffηx,y,y=0,indep=x,y,dep=ξ,η

T2ξx=0,ξy=0,ηx=0,ηy=0,indep=x,y,dep=ξ,η

(2)

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

(3)

Construct LAVFs for 2-dim Euclidean group E(2) and 2-dim translation group T(2).

LE2LAVFV,E2

LE2ξx+ηy&whereξy,y=0,ξx=0,ηx=ξy,ηy=0

(4)

LT2LAVFV,T2

LT2ξx+ηy&whereξx=0,ηx=0,ξy=0,ηy=0

(5)

Both LAVFs are Lie algebras.

IsLieAlgebraLE2

true

(6)

IsLieAlgebraLT2

true

(7)

LT2 is invariant under the action of LE2.

IsInvariantLT2,LE2

true

(8)

Compatibility

• 

The IsInvariant 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]

IsLieAlgebra