The GetParametricDerivatives method gets the parametric derivatives of a LHPDEs system that have been recorded in an IDBasis object as a fixed basis variables.

Let B be an IDBasis object that is associated with LHPDE object S. Then GetParametricDerivatives(B) returns a list of parametric derivatives of S.

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

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

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

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

$\mathrm{E2}≔\mathrm{LHPDE}\left(\left[\frac{{\partial }^2}{\partial y^2}\mathrm{\ξ}\left(x\,y\right)\=0\,\frac{\partial }{\partial x}\mathrm{\η}\left(x\,y\right)\=-\left(\frac{\partial }{\partial y}\mathrm{\ξ}\left(x\,y\right)\right)\,\frac{\partial }{\partial y}\mathrm{\η}\left(x\,y\right)\=0\,\frac{\partial }{\partial x}\mathrm{\ξ}\left(x\,y\right)\=0\right]\,\mathrm{indep}\=\left[x\,y\right]\,\mathrm{dep}\=\left[\mathrm{\ξ}\,\mathrm{\η}\right]\right)$

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

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

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

$B≔\mathrm{IDBasis}\left(\mathrm{E2}\,\left[\mathrm{\ξ}\left(x\,y\right)-y\left(\frac{\partial }{\partial y}\mathrm{\ξ}\left(x\,y\right)\right)\,\mathrm{\η}\left(x\,y\right)-x\left(\frac{\partial }{\partial y}\mathrm{\ξ}\left(x\,y\right)\right)\,-\left(\frac{\partial }{\partial y}\mathrm{\ξ}\left(x\,y\right)\right)\right]\right)$

$B≔\left[\mathrm{\xi }-y\left({\mathrm{\xi }}_y\right)\,\mathrm{\eta }-x\left({\mathrm{\xi }}_y\right)\,-{\mathrm{\xi }}_y\right]$

$\mathrm{GetParametricDerivatives}\left(B\right)$

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

The GetParametricDerivatives command was introduced in Maple 2020.

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