Copy
clone a LAVF object to have different infinitesimal (and constant of variables) names
Calling Sequence
Parameters
Description
Examples
Compatibility
Copy( obj, vars)
obj
-
LAVF objects.
vars
a name or a list of names
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.
withLieAlgebrasOfVectorFields:
Typesetting:-Settingsuserep=true
false
Typesetting:-Suppressξx,y,ηx,y,αx,y,βx,y,φx,y
V≔VectorFieldξx,yDx+ηx,yDy,space=x,y
V≔ξⅆⅆx+ηⅆⅆy
E2≔LHPDEdiffξx,y,y,y=0,diffηx,y,x=−diffξx,y,y,diffηx,y,y=0,diffξx,y,x=0,indep=x,y,dep=ξ,η
E2≔ξy,y=0,ηx=−ξy,ηy=0,ξx=0,indep=x,y,dep=ξ,η
Case 1: A vector fields system for E(2).
L≔LAVFV,E2
L≔ξⅆⅆx+ηⅆⅆy&whereξy,y=0,ξx=0,ηx=−ξy,ηy=0
CopyL,α,β
αⅆⅆx+βⅆⅆy&whereαy,y=0,αx=0,βx=−αy,βy=0
Case2 : A vector fields system for E(2) that has been fully integrated.
Lsol≔LAVFSolveL,output=lavf
Lsol≔ξⅆⅆx+ηⅆⅆy&whereξ=−c__1y+c__3,η=c__1x+c__2
Lsol includes infinitesimals (ξ,η) and constants of integration _C1, _C2, _C3
DQ≔GetDeterminingSystemLsol
DQ≔ξ=−c__1y+c__3,η=c__1x+c__2,indep=x,y,dep=ξ,η,c__1,c__2,c__3
CopyLsol,α,β,a,b,c
αⅆⅆx+βⅆⅆy&whereα=−ay+c,β=ax+b
CopyLsol,φ
φ1x,yⅆⅆx+φ2x,yⅆⅆy&whereφ1x,y=−yφ3+φ5,φ2x,y=xφ3+φ4
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
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