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

Copy

clone a LAVF object to have different infinitesimal (and constant of variables) names

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

Copy( obj, vars)

Parameters

obj

-

LAVF objects.

vars

-

a name or a list of names

Description

• 

Let L be a LAVF object with n; infinitesimal variables and k; (or maybe none) constants of integration variables. Then the Copy method clones L and returns a new LAVF object with new infinitesimals and constants of integration variable names as given in vars. The new variable names vars will replace the ones from the object.

• 

If vars is given as a list of names, then the number of entries in vars must be n+k; (i.e. same as the number of dependent variables from the determining system of L) (see GetDependents).

• 

If vars is given as one single name ξ, then the new variables names will be ξ1,ξ2,,ξn+k.

• 

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

Examples

withLieAlgebrasOfVectorFields:

Typesetting:-Settingsuserep=true

false

(1)

Typesetting:-Suppressξx,y,ηx,y,αx,y,βx,y,φx,y

VVectorFieldξx,yDx+ηx,yDy,space=x,y

Vξx+ηy

(2)

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

(3)

Case 1: A vector fields system for E(2).

LLAVFV,E2

Lξx+ηy&whereξy,y=0,ξx=0,ηx=ξy,ηy=0

(4)

CopyL,α,β

αx+βy&whereαy,y=0,αx=0,βx=αy,βy=0

(5)

Case2 : A vector fields system for E(2) that has been fully integrated.

LsolLAVFSolveL,output=lavf

Lsolξx+ηy&whereξ=_C1y+_C3,η=_C1x+_C2

(6)

Lsol includes infinitesimals (ξ,η) and constants of integration _C1, _C2, _C3

DQGetDeterminingSystemLsol

DQξ=_C1y+_C3,η=_C1x+_C2,indep=x,y,dep=ξ,η,_C1,_C2,_C3

(7)

CopyLsol,α,β,a,b,c

αx+βy&whereα=ay+c,β=ax+b

(8)

CopyLsol,φ

φ1x,yx+φ2x,yy&whereφ1x,y=yφ3+φ5,φ2x,y=xφ3+φ4

(9)

Compatibility

• 

The Copy 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]

GetDependents