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VectorSpaceSum

find a LHPDE object whose solution space is the sum of the solution spaces of given LHPDE objects.

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

VectorSpaceSum( obj1, obj2, ..., depname = vars )

Parameters

obj1, obj2, ...

-

a sequence of LHPDE objects living on the same space

vars

-

(optional) a list of new dependent variable names

Description

• 

Let obj1, obj2, ... be a sequence of LHPDE objects living on the same space (see AreSameSpace). The VectorSpaceSum method finds a LHPDEs system whose solution space is the vector space sum of solution spaces of obj1,obj2,....

• 

The method returns a rif-reduced LHPDE object.

• 

By default, the dependent variable names of the returned object are taken from obj1. The dependent variable names will be vars if the optional argument depname = vars is specified.

• 

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

Examples

withLieAlgebrasOfVectorFields:

Typesetting:-Settingsuserep=true:

Typesetting:-Suppressα,β,η,φ,ψ,ξx,y:

SLHPDEdiffξx,y,x=0,diffηx,y,y=0,diffξx,y,y+diffηx,y,x=0,diffξx,y,y,y=0,diffηx,y,x,x=0

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

(1)

S1LHPDEdiffαx,y,x,x=0,diffαx,y,y=0,diffβx,y,x=0,diffβx,y,y,y=0,diffαx,y,xdiffβx,y,y=0,indep=x,y,dep=α,β

S1αx,x=0,αy=0,βx=0,βy,y=0,αxβy=0,indep=x,y,dep=α,β

(2)

VectorSpaceSumS,S1

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

(3)

VectorSpaceSumS,S1,depname=φ,ψ

φx,x=0,φy=0,ψy,y=0,ψx=0,indep=x,y,dep=φ,ψ

(4)

Compatibility

• 

The VectorSpaceSum 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]

AreSameSpace