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.

$\mathrm{with}\left(\mathrm{LieAlgebrasOfVectorFields}\right)\:$

$\mathrm{Typesetting}:-\mathrm{Settings}\left(\mathrm{userep}=\mathrm{true}\right)\:$

$\mathrm{Typesetting}:-\mathrm{Suppress}\left(\left[\mathrm{\xi }\left(x\,y\right)\,\mathrm{\eta }\left(x\,y\right)\right]\right)\:$

$\mathrm{E2}≔\mathrm{LHPDE}\left(\left[\mathrm{diff}\left(\mathrm{\xi }\left(x\,y\right)\,y\,y\right)=0\,\mathrm{diff}\left(\mathrm{\eta }\left(x\,y\right)\,x\right)=-\mathrm{diff}\left(\mathrm{\xi }\left(x\,y\right)\,y\right)\,\mathrm{diff}\left(\mathrm{\eta }\left(x\,y\right)\,y\right)=0\,\mathrm{diff}\left(\mathrm{\xi }\left(x\,y\right)\,x\right)=0\right]\,\mathrm{indep}=\left[x\,y\right]\,\mathrm{dep}=\left[\mathrm{\xi }\,\mathrm{\eta }\right]\right)$

$\mathrm{E2}≔\left[{\mathrm{\xi }}_{y,y}=0\,{\mathrm{\eta }}_x=-{\mathrm{\xi }}_y\,{\mathrm{\eta }}_y=0\,{\mathrm{\xi }}_x=0\right],\mathrm{indep}=\left[x\,y\right],\mathrm{dep}=\left[\mathrm{\xi }\,\mathrm{\eta }\right]$

$\mathrm{IsFiniteType}\left(\mathrm{E2}\right)$

$\mathrm{true}$

$\mathrm{ParametricDerivatives}\left(\mathrm{E2}\right)$

$\left[\mathrm{\xi }\,{\mathrm{\xi }}_y\,\mathrm{\eta }\right]$

$\mathrm{E2red}≔\mathrm{RifReduce}\left(\mathrm{E2}\,\left[\mathrm{\xi }\,\mathrm{\eta }\right]\right)$

$\mathrm{E2red}≔\left[{\mathrm{\xi }}_{y,y}=0\,{\mathrm{\xi }}_x=0\,{\mathrm{\eta }}_x=-{\mathrm{\xi }}_y\,{\mathrm{\eta }}_y=0\right],\mathrm{indep}=\left[x\,y\right],\mathrm{dep}=\left[\mathrm{\xi }\,\mathrm{\eta }\right]$

$\mathrm{IsRifReduced}\left(\mathrm{E2red}\right)$

$\mathrm{true}$

$\mathrm{IsTotalDegreeRanking}\left(\mathrm{E2red}\right)$

$\mathrm{true}$

$\mathrm{ParametricDerivatives}\left(\mathrm{E2}\,\mathrm{order}=0..0\right)$

$\left[\mathrm{\xi }\,\mathrm{\eta }\right]$

The ParametricDerivatives command was introduced in Maple 2020.

For more information on Maple 2020 changes, see Updates in Maple 2020.