 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

 > $\mathrm{with}\left(\mathrm{LieAlgebrasOfVectorFields}\right):$
 > $\mathrm{Typesetting}:-\mathrm{Settings}\left(\mathrm{userep}=\mathrm{true}\right):$
 > $\mathrm{Typesetting}:-\mathrm{Suppress}\left(\left[\mathrm{ξ}\left(x,y\right),\mathrm{η}\left(x,y\right)\right]\right)$
 > $\mathrm{E2}≔\mathrm{LHPDE}\left(\left[\frac{{\partial }^{2}}{\partial {y}^{2}}\mathrm{ξ}\left(x,y\right)=0,\frac{\partial }{\partial x}\mathrm{η}\left(x,y\right)=-\left(\frac{\partial }{\partial y}\mathrm{ξ}\left(x,y\right)\right),\frac{\partial }{\partial y}\mathrm{η}\left(x,y\right)=0,\frac{\partial }{\partial x}\mathrm{ξ}\left(x,y\right)=0\right],\mathrm{indep}=\left[x,y\right],\mathrm{dep}=\left[\mathrm{ξ},\mathrm{η}\right]\right)$
 ${\mathrm{E2}}{≔}\left[{{\mathrm{\xi }}}_{{y}{,}{y}}{=}{0}{,}{{\mathrm{\eta }}}_{{x}}{=}{-}{{\mathrm{\xi }}}_{{y}}{,}{{\mathrm{\eta }}}_{{y}}{=}{0}{,}{{\mathrm{\xi }}}_{{x}}{=}{0}\right]{,}{\mathrm{indep}}{=}\left[{x}{,}{y}\right]{,}{\mathrm{dep}}{=}\left[{\mathrm{\xi }}{,}{\mathrm{\eta }}\right]$ (1)
 > $\mathrm{ParametricDerivatives}\left(\mathrm{E2}\right)$
 $\left[{\mathrm{\xi }}{,}{{\mathrm{\xi }}}_{{y}}{,}{\mathrm{\eta }}\right]$ (2)
 > $B≔\mathrm{IDBasis}\left(\mathrm{E2},\left[\mathrm{ξ}\left(x,y\right)-y\left(\frac{\partial }{\partial y}\mathrm{ξ}\left(x,y\right)\right),\mathrm{η}\left(x,y\right)-x\left(\frac{\partial }{\partial y}\mathrm{ξ}\left(x,y\right)\right),-\left(\frac{\partial }{\partial y}\mathrm{ξ}\left(x,y\right)\right)\right]\right)$
 ${B}{≔}\left[{\mathrm{\xi }}{-}{y}{}\left({{\mathrm{\xi }}}_{{y}}\right){,}{\mathrm{\eta }}{-}{x}{}\left({{\mathrm{\xi }}}_{{y}}\right){,}{-}{{\mathrm{\xi }}}_{{y}}\right]$ (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.