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
VectorSpaceSum( obj1, obj2, ..., depname = vars )
obj1, obj2, ...
-
a sequence of LHPDE objects living on the same space
vars
(optional) a list of new dependent variable names
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.
withLieAlgebrasOfVectorFields:
Typesetting:-Settingsuserep=true:
Typesetting:-Suppressα,β,η,φ,ψ,ξx,y:
S≔LHPDEdiffξx,y,x=0,diffηx,y,y=0,diffξx,y,y+diffηx,y,x=0,diffξx,y,y,y=0,diffηx,y,x,x=0
S≔ξx=0,ηy=0,ξy+ηx=0,ξy,y=0,ηx,x=0,indep=x,y,dep=η,ξ
S1≔LHPDEdiffαx,y,x,x=0,diffαx,y,y=0,diffβx,y,x=0,diffβx,y,y,y=0,diffαx,y,x−diffβx,y,y=0,indep=x,y,dep=α,β
S1≔αx,x=0,αy=0,βx=0,βy,y=0,αx−βy=0,indep=x,y,dep=α,β
VectorSpaceSumS,S1
ηx,x=0,ηy=0,ξy,y=0,ξx=0,indep=x,y,dep=η,ξ
VectorSpaceSumS,S1,depname=φ,ψ
φx,x=0,φy=0,ψy,y=0,ψx=0,indep=x,y,dep=φ,ψ
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
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