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SolutionDimension

calculate the solution dimension for a LAVF object.

IsFiniteType

check if a LAVF object is of finite type

IsTrivial

check if a LAVF object has only the trivial solution

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

SolutionDimension( obj)

IsFiniteType( obj)

IsTrivial( obj)

Parameters

obj

-

a LAVF object

Description

• 

The SolutionDimension method calculates the solution dimension of the determining system for a LAVF object. It returns  if the solution dimension is not finite.

• 

Let L be a LAVF object. Then IsFiniteType(L) returns true if and only if SolutionDimension(L) < .

• 

Let L be a LAVF object. Then IsTrivial(L) returns true if and only if SolutionDimension(L) = 0.

• 

These methods are front-end to the corresponding methods of a LHPDE object. That is, let L be a LAVF object and S be its determining system (i.e.  S = GetDeterminingSystem(L)), then SolutionDimension(L) equals SolutionDimension(S), IsFiniteType(L) equals IsFiniteType(S) and IsTrivial(L) equals IsTrivial(S). For more detail, see the corresponding methods: SolutionDimension, IsFiniteType, IsTrivial of a LHPDE object.

• 

These methods are associated with the LAVF object. For more detail, see Overview of the LAVF object.

Examples

withLieAlgebrasOfVectorFields&colon;

Typesetting:-Settingsuserep=true&colon;

Typesetting:-Suppressξx&comma;y&comma;ηx&comma;y&colon;

First, construct an indeterminate vector field and a determining system, then construct an LAVF object from them...

VVectorFieldξx&comma;yDx+ηx&comma;yDy&comma;space=x&comma;y

Vξx+ηy

(1)

E2LHPDEdiffξx&comma;y&comma;y&comma;y=0&comma;diffηx&comma;y&comma;x=diffξx&comma;y&comma;y&comma;diffηx&comma;y&comma;y=0&comma;diffξx&comma;y&comma;x=0&comma;indep=x&comma;y&comma;dep=ξ&comma;η

E2ξy,y=0&comma;ηx=ξy&comma;ηy=0&comma;ξx=0,indep=x&comma;y,dep=ξ&comma;η

(2)

LLAVFV&comma;E2

Lξx+ηy&whereξy,y=0&comma;ξx=0&comma;ηx=ξy&comma;ηy=0

(3)

Now we can apply the methods to see properties of L.

SolutionDimensionL

3

(4)

The determining system of L is of finite type but not trivial:

IsFiniteTypeL

true

(5)

IsTrivialL

false

(6)

Compatibility

• 

The SolutionDimension, IsFiniteType and IsTrivial commands were introduced in Maple 2020.

• 

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

See Also

LAVF (Object overview)

LieAlgebrasOfVectorFields[VectorField]

LieAlgebrasOfVectorFields[LHPDE]

LieAlgebrasOfVectorFields[LAVF]

SolutionDimension

IsFiniteType

IsTrivial