ParametricDerivatives
find the parametric derivatives of a LAVF object
Calling Sequence
Parameters
Description
Examples
Compatibility
ParametricDerivatives( obj)
ParametricDerivatives( obj, order= m .. n)
ParametricDerivatives( obj, order= m)
obj
-
a LAVF object
m, n
non-negative integers
The ParametricDerivatives method finds the parametric derivatives of a LAVF object. The parametric derivatives are returned as a list of functions.
The method is front-end to the corresponding method of a LHPDE object. That is, let L be a LAVF object and S be its determining system as a LHPDE object (i.e. S = GetDeterminingSystem(L)), then the call ParametricDerivatives(L) is equivalent to ParametricDerivatives(S). All remaining input arguments will be passed down to its determining system S level. See the method ParametricDerivatives of a LHPDE object for more detail.
This method is associated with the LAVF object. For more detail, see Overview of the LAVF object.
withLieAlgebrasOfVectorFields:
Typesetting:-Settingsuserep=true:
Typesetting:-Suppressξx,y,ηx,y:
First, construct an indeterminate vector field and a determining system, then construct an LAVF object from them...
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
L≔LAVFV,E2
L≔ξⅆⅆx+ηⅆⅆy&whereξy,y=0,ξx=0,ηx=−ξy,ηy=0
Now we can find the parametric derivatives of L...
ParametricDerivativesL
η,ξ,ξy
ParametricDerivativesL,order=0
ξ,η
The ParametricDerivatives command was 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]
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