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IsSubspace

check if solution space of a LAVF object is subspace of solution space of another LAVF object.

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

IsSubspace( L1, L2)

Parameters

L1, L2

-

LAVF objects

Description

• 

Let L1, L2 be LAVF objects, the IsSubspace returns true if solution space of L1 is a subspace of solution space of L2. False otherwise.

• 

More precisely, the method returns true if at each point x0, the local solution space of L1 at x0 is a subspace of the local solution space of L2 at x0.

• 

This method eventually pass tasks down to IsSubspace of the LHPDE object

• 

The determining systems of input arguments L1 and L2 need not have the same dependent variable names or dependencies.

• 

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)

C2LHPDEdiffξx,y,x,x=0,diffξx,y,x,y=0,diffξx,y,y,y=0,diffηx,y,x=diffξx,y,y,diffηx,y,y=diffξx,y,x,indep=x,y,dep=ξ,η

C2ξx,x=0,ξx,y=0,ξy,y=0,ηx=ξy,ηy=ξx,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)

We first construct two LAVF objects for C2 and E2

LC2LAVFV,C2

LC2ξx+ηy&whereξy,y=0,ηy,y=0,ξx=ηy,ηx=ξy

(4)

LE2LAVFV,E2

LE2ξx+ηy&whereξy,y=0,ξx=0,ηx=ξy,ηy=0

(5)

IsSubspaceLE2,LC2

true

(6)

The determining system of this LAVF object's dependent variables have different names and dependencies.

VaVectorFieldαyDx+βxDy,space=x,y

Vaαyx+βxy

(7)

E2pLHPDEdiffαy,y,y=0,diffβx,x=diffαy,y,indep=x,y,dep=α,β

E2pⅆ2ⅆy2αy=0,ⅆⅆxβx=ⅆⅆyαy,indep=x,y,dep=αy,βx

(8)

LE2pLAVFVa,E2p

LE2pαyx+βxy&whereⅆ2ⅆy2αy=0,ⅆⅆxβx=ⅆⅆyαy

(9)

IsSubspaceLE2p,LC2

true

(10)

Compatibility

• 

The IsSubspace 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]

IsSubspace