LAVF Object Overloaded builtins - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Differential Equations : Lie Symmetry Method : Commands for PDEs (and ODEs) : LieAlgebrasOfVectorFields : LAVF : LieAlgebrasOfVectorFields/LAVF/Builtins

LAVF Object Overloaded builtins

overview of overloaded builtins for LAVF object.

 

Description

Examples

Compatibility

Description

• 

The functionalities of some Maple builtin commands are extended for use on LAVF object.

• 

The following builtins have been overloaded for this purpose: indets, has, type, hastype

• 

Let L be a LAVF object.

• 

(i) The call type(L, t) returns true if t is any of the following types: module, object, anything, and LAVF. See examples below.

• 

(ii) The call type(L, dependent(x)) and type(L, freeof(x)) respectively return true if its determining system S including the DEs system, the independent variables, and the dependent variables of S contain (respectively don't contain) x. See example below.

• 

The indets, has, hastype builtin commands accept a LAVF object and apply their methods onto the DEs system, the independent variables, and the dependent variables of the determining system of the LAVF object.

• 

These overloaded builtins 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:

VVectorFieldξx,yDx+ηx,yDy,space=x,y

Vξx+ηy

(1)

E2LHPDEdiffξx,y,x=0,diffηx,y,y=0,diffξx,y,y+diffηx,y,x=0,diffξx,y,y,y=0,diffηx,y,x,x=0,indep=x,y,dep=ξ,η

E2ξx=0,ηy=0,ξy+ηx=0,ξy,y=0,ηx,x=0,indep=x,y,dep=ξ,η

(2)

We first construct a LAVF object for 2-dim Euclidean group E(2)

LLAVFV,E2

Lξx+ηy&whereξy,y=0,ξx=0,ηx=ξy,ηy=0

(3)

We also construct a fully-integrated LAVF object for E(2).

LsolLAVFSolveL,output=lavf,consts=a,b,c

Lsolξx+ηy&whereξ=ay+c,η=ax+b

(4)

type

typeL,LAVF

true

(5)

typeL,object

true

(6)

typeL,`module`

true

(7)

typeL,dependentx

true

(8)

typeL,freeofx

false

(9)

and the fully-integrated LAVF Lsol does contain constant of integration variable a.

typeLsol,dependenta

true

(10)

indets, has, hastype

indetsL

x,y,ξy,y,ηx,ηy,ξx,ξy,η,ξ

(11)

indetsLsol

a,b,c,x,y,η,ξ

(12)

hasL,b

false

(13)

hasLsol,b

true

(14)

hastypeL,scalar

true

(15)

hastypeLsol,float

false

(16)

Compatibility

• 

The LAVF Object Overloaded builtins 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]

type

indets

has

hastype