GetParametricDerivatives - Maple Help

GetParametricDerivatives

get the parametric derivatives of a LHPDEs system that is associated with an IDBasis object

 Calling Sequence GetParametricDerivatives( B)

Parameters

 B - IDBasis object

Description

 • 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.

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)
 > $\mathrm{ParametricDerivatives}\left(\mathrm{E2}\right)$
 $\left[{\mathrm{\xi }}{,}{{\mathrm{\xi }}}_{{y}}{,}{\mathrm{\eta }}\right]$ (2)
 > $B≔\mathrm{IDBasis}\left(\mathrm{E2},\left[\mathrm{\xi }\left(x,y\right)-y\mathrm{diff}\left(\mathrm{\xi }\left(x,y\right),y\right),\mathrm{\eta }\left(x,y\right)-x\mathrm{diff}\left(\mathrm{\xi }\left(x,y\right),y\right),-\mathrm{diff}\left(\mathrm{\xi }\left(x,y\right),y\right)\right]\right)$
 ${B}{≔}\left[{\mathrm{\xi }}{-}{y}{}\left({{\mathrm{\xi }}}_{{y}}\right){,}{\mathrm{\eta }}{-}{x}{}\left({{\mathrm{\xi }}}_{{y}}\right){,}{-}{{\mathrm{\xi }}}_{{y}}\right]$ (3)
 > $\mathrm{GetParametricDerivatives}\left(B\right)$
 $\left[{\mathrm{\xi }}{,}{{\mathrm{\xi }}}_{{y}}{,}{\mathrm{\eta }}\right]$ (4)

Compatibility

 • The GetParametricDerivatives command was introduced in Maple 2020.