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IsSubspace

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

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

IsSubspace( obj1, obj2)

Parameters

obj1

-

a LHPDE object that is assumed to be in rif-reduced form (see IsRifReduced)

obj2

-

a LHPDE object

Description

• 

The IsSubspace method returns true if solution space of obj1 is a subspace of solution space of obj2. False otherwise.

• 

More precisely, the method returns true if at each point x0, the local solution space of obj1  at x0 is a subspace of the local solution space of obj2 at x0.

• 

The input arguments obj1 and obj2 need not have the same dependent variable names or dependencies.

• 

This method is associated with the LHPDE object. For more detail, see Overview of the LHPDE object.

Examples

withLieAlgebrasOfVectorFields:

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,inRifReducedForm=true

C22x2ξx,y=0,2xyξx,y=0,2y2ξx,y=0,xηx,y=yξx,y,yηx,y=xξx,y,indep=x,y,dep=ξx,y,ηx,y

(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,inRifReducedForm=true

E22y2ξx,y=0,xηx,y=yξx,y,yηx,y=0,xξx,y=0,indep=x,y,dep=ξx,y,ηx,y

(2)

IsSubspaceE2,C2

true

(3)

This LHPDE object's dependent variables have different names and dependencies.

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

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

(4)

IsSubspaceE2p,C2

true

(5)

Compatibility

• 

The IsSubspace command was introduced in Maple 2020.

• 

For more information on Maple 2020 changes, see Updates in Maple 2020.

See Also

LHPDE (Object overview)

LieAlgebrasOfVectorFields[LHPDE]

IsRifReduced