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GetVectorField

get the vector field of a LAVF object

GetDeterminingSystem

 get the symmetry determining system of a LAVF object

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

GetVectorField( obj)

GetDeterminingSystem( obj)

Parameters

obj

-

a LAVF object

Description

• 

The GetVectorField method returns the vector field for a LAVF object, as a VectorField object. The returned VectorField object then has access to various methods. See Overview of the VectorField object for more detail.

• 

The GetDeterminingSystem method returns the symmetry determining system for a LAVF object, as a LHPDE object. The returned LHPDE object then has access to various methods. See Overview of the LHPDE object for more detail.

• 

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

Examples

withLieAlgebrasOfVectorFields:

Typesetting:-Settingsuserep=true:

Typesetting:-Suppressξx,y,ηx,y:

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

VVectorFieldξx,yDx+ηx,yDy,space=x,y

Vξx+ηy

(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

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

(2)

LLAVFV,E2

Lξx+ηy&whereξy,y=0,ξx=0,ηx=ξy,ηy=0

(3)

Now we can retrieve the basic properties of the LAVF L:

GetVectorFieldL

ξx+ηy

(4)

SGetDeterminingSystemL

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

(5)

The determining system of L is indeed a LHPDE object, and has access to various methods...

typeS,LHPDE

true

(6)

GetSystemS

ξy,y=0,ξx=0,ηx=ξy,ηy=0

(7)

GetDependentsS

ξ,η

(8)

GetIndependentsS

x,y

(9)

Compatibility

• 

The GetVectorField and GetDeterminingSystem commands were introduced in Maple 2020.

• 

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

See Also

LAVF (Object overview)

VectorField (Object overview)

LHPDE (Object overview)

LieAlgebrasOfVectorFields[VectorField]

LieAlgebrasOfVectorFields[LHPDE]

LieAlgebrasOfVectorFields[LAVF]