ParametricDerivatives - Maple Help

ParametricDerivatives

find the parametric derivatives of a LHPDE object

 Calling Sequence ParametricDerivatives( obj) ParametricDerivatives( obj, order= m .. n) ParametricDerivatives( obj, order= m)

Parameters

 obj - a LHPDE object m, n - non-negative integers

Description

 • The ParametricDerivatives method finds the parametric derivatives of a LHPDE object. The parametric derivatives are returned as a list of functions.
 • In the first calling sequence, the method returns all parametric derivatives of a LHPDE object.
 • The LHPDE object in the first calling sequence must be of finite type (has finite-dimensional solution space, see IsFiniteType).
 • In the second and third calling sequences, the method returns the parametric derivatives of a LHPDE object for a specific order: from m to n inclusive (or of order exactly m respectively).
 • The LHPDE object in the second and third calling sequences must be in rif-reduced form (see IsRifReduced) with respect to a total degree ranking (see IsTotalDegreeRanking).
 • The method ParametricDerivatives internally uses the existing Maple command DEtools[initialdata] for computing parametric derivatives.
 • This method is associated with the LHPDE object. For more detail, see Overview of the LHPDE object.

Examples

 > $\mathrm{with}\left(\mathrm{LieAlgebrasOfVectorFields}\right):$
 > $\mathrm{Typesetting}:-\mathrm{Settings}\left(\mathrm{userep}=\mathrm{true}\right):$
 > $\mathrm{Typesetting}:-\mathrm{Suppress}\left(\left[\mathrm{\xi }\left(x,y\right),\mathrm{\eta }\left(x,y\right)\right]\right):$
 > $\mathrm{E2}≔\mathrm{LHPDE}\left(\left[\mathrm{diff}\left(\mathrm{\xi }\left(x,y\right),y,y\right)=0,\mathrm{diff}\left(\mathrm{\eta }\left(x,y\right),x\right)=-\mathrm{diff}\left(\mathrm{\xi }\left(x,y\right),y\right),\mathrm{diff}\left(\mathrm{\eta }\left(x,y\right),y\right)=0,\mathrm{diff}\left(\mathrm{\xi }\left(x,y\right),x\right)=0\right],\mathrm{indep}=\left[x,y\right],\mathrm{dep}=\left[\mathrm{\xi },\mathrm{\eta }\right]\right)$
 ${\mathrm{E2}}{≔}\left[{{\mathrm{\xi }}}_{{y}{,}{y}}{=}{0}{,}{{\mathrm{\eta }}}_{{x}}{=}{-}{{\mathrm{\xi }}}_{{y}}{,}{{\mathrm{\eta }}}_{{y}}{=}{0}{,}{{\mathrm{\xi }}}_{{x}}{=}{0}\right]{,}{\mathrm{indep}}{=}\left[{x}{,}{y}\right]{,}{\mathrm{dep}}{=}\left[{\mathrm{\xi }}{,}{\mathrm{\eta }}\right]$ (1)
 > $\mathrm{IsFiniteType}\left(\mathrm{E2}\right)$
 ${\mathrm{true}}$ (2)
 > $\mathrm{ParametricDerivatives}\left(\mathrm{E2}\right)$
 $\left[{\mathrm{\xi }}{,}{{\mathrm{\xi }}}_{{y}}{,}{\mathrm{\eta }}\right]$ (3)
 > $\mathrm{E2red}≔\mathrm{RifReduce}\left(\mathrm{E2},\left[\mathrm{\xi },\mathrm{\eta }\right]\right)$
 ${\mathrm{E2red}}{≔}\left[{{\mathrm{\xi }}}_{{y}{,}{y}}{=}{0}{,}{{\mathrm{\xi }}}_{{x}}{=}{0}{,}{{\mathrm{\eta }}}_{{x}}{=}{-}{{\mathrm{\xi }}}_{{y}}{,}{{\mathrm{\eta }}}_{{y}}{=}{0}\right]{,}{\mathrm{indep}}{=}\left[{x}{,}{y}\right]{,}{\mathrm{dep}}{=}\left[{\mathrm{\xi }}{,}{\mathrm{\eta }}\right]$ (4)
 > $\mathrm{IsRifReduced}\left(\mathrm{E2red}\right)$
 ${\mathrm{true}}$ (5)
 > $\mathrm{IsTotalDegreeRanking}\left(\mathrm{E2red}\right)$
 ${\mathrm{true}}$ (6)
 > $\mathrm{ParametricDerivatives}\left(\mathrm{E2},\mathrm{order}=0..0\right)$
 $\left[{\mathrm{\xi }}{,}{\mathrm{\eta }}\right]$ (7)

Compatibility

 • The ParametricDerivatives command was introduced in Maple 2020.