VectorSpaceSum - Maple Help
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VectorSpaceSum

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

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

VectorSpaceSum( L1, L2, ..., depname = vars )

Parameters

L1, L2, ...

-

a sequence of LAVF objects living on the same space (see AreSameSpace)

vars

-

(optional) a list of new dependent variable names

Description

• 

Let L1,L2, ... be a sequence of LAVF objects living on the same space. The VectorSpaceSum method finds a LAVF object whose solution space is the vector space sum of solution spaces of L1,L2,....

• 

By default, the dependent variable names of the returned object are taken from L1. The dependent variable names will be vars if the optional argument depnames = vars is specified.

• 

This method is front-end to the corresponding method of a LHPDE object. That is, let S1, S2,... be the determining systems of L1,L2,...  (i.e.  Si = GetDeterminingSystem(Li)), then the call VectorSpaceSum(L1,L2,..) is equivalent to VectorSpaceSum(S1,S2,..). All remaining input arguments will be passed down to its determining system level. See the method VectorSpaceSum of a LHPDE object for more detail.

• 

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

Examples

(1)

The determining system for 2-dim Euclidean

(2)

The determining system for 2-dim translations

(3)

We first construct LAVFs for E(2) and T(2)

(4)

(5)

(6)

(7)

Compatibility

• 

The VectorSpaceSum 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]

AreSameSpace

VectorSpaceSum

 


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