CleanDependencies - Maple Help

CleanDependencies

remove any redundant dependant variables from a LAVF object.

 Calling Sequence CleanDependencies( obj)

Parameters

 obj - a LAVF object

Description

 • The CleanDependencies method returns a new LAVF object with any redundant dependant variables or constant of integration removed from its Lie determining system and the corresponding vector field.
 • This method is associated with the LAVF object. For more detail, see Overview of the LAVF object.

Examples

 > $\mathrm{with}\left(\mathrm{LieAlgebrasOfVectorFields}\right):$
 > $V≔\mathrm{VectorField}\left(\mathrm{\xi }\left(x,y\right)\mathrm{D}\left[x\right]+\mathrm{\eta }\left(x,y\right)\mathrm{D}\left[y\right],\mathrm{space}=\left[x,y\right]\right)$
 ${V}{≔}{\mathrm{\xi }}{}\left({x}{,}{y}\right){}\frac{{\partial }}{{\partial }{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{+}{\mathrm{\eta }}{}\left({x}{,}{y}\right){}\frac{{\partial }}{{\partial }{y}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}$ (1)
 > $\mathrm{E2}≔\mathrm{LHPDE}\left(\left[\mathrm{diff}\left(\mathrm{\xi }\left(x,y\right),y,y\right)=0,\mathrm{diff}\left(\mathrm{\eta }\left(x,y\right),x\right)=-\mathrm{diff}\left(\mathrm{\xi }\left(x,y\right),y\right),\mathrm{diff}\left(\mathrm{\eta }\left(x,y\right),y\right)=0,\mathrm{diff}\left(\mathrm{\xi }\left(x,y\right),x\right)=0,\mathrm{c1}=0,\mathrm{c2}=0\right],\mathrm{indep}=\left[x,y\right],\mathrm{dep}=\left[\mathrm{\xi },\mathrm{\eta },\mathrm{c1},\mathrm{c2}\right]\right)$
 ${\mathrm{E2}}{≔}\left[\frac{{{\partial }}^{{2}}}{{\partial }{{y}}^{{2}}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{\xi }}{}\left({x}{,}{y}\right){=}{0}{,}\frac{{\partial }}{{\partial }{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{\eta }}{}\left({x}{,}{y}\right){=}{-}\frac{{\partial }}{{\partial }{y}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{\xi }}{}\left({x}{,}{y}\right){,}\frac{{\partial }}{{\partial }{y}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{\eta }}{}\left({x}{,}{y}\right){=}{0}{,}\frac{{\partial }}{{\partial }{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{\xi }}{}\left({x}{,}{y}\right){=}{0}{,}{\mathrm{c1}}{=}{0}{,}{\mathrm{c2}}{=}{0}\right]{,}{\mathrm{indep}}{=}\left[{x}{,}{y}\right]{,}{\mathrm{dep}}{=}\left[{\mathrm{\xi }}{}\left({x}{,}{y}\right){,}{\mathrm{\eta }}{}\left({x}{,}{y}\right){,}{\mathrm{c1}}{,}{\mathrm{c2}}\right]$ (2)
 > $L≔\mathrm{LAVF}\left(V,\mathrm{E2}\right)$
 ${L}{≔}\left[{\mathrm{\xi }}{}\left({x}{,}{y}\right){}\frac{{\partial }}{{\partial }{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{+}{\mathrm{\eta }}{}\left({x}{,}{y}\right){}\frac{{\partial }}{{\partial }{y}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}\right]\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{&where}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\left\{\left[\frac{{{\partial }}^{{2}}}{{\partial }{{y}}^{{2}}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{\xi }}{}\left({x}{,}{y}\right){=}{0}{,}\frac{{\partial }}{{\partial }{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{\xi }}{}\left({x}{,}{y}\right){=}{0}{,}\frac{{\partial }}{{\partial }{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{\eta }}{}\left({x}{,}{y}\right){=}{-}\frac{{\partial }}{{\partial }{y}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{\xi }}{}\left({x}{,}{y}\right){,}\frac{{\partial }}{{\partial }{y}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{\eta }}{}\left({x}{,}{y}\right){=}{0}{,}{\mathrm{c1}}{=}{0}{,}{\mathrm{c2}}{=}{0}\right]\right\}$ (3)
 > $\mathrm{CleanDependencies}\left(L\right)$
 $\left[{\mathrm{\xi }}{}\left({x}{,}{y}\right){}\frac{{\partial }}{{\partial }{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{+}{\mathrm{\eta }}{}\left({x}{,}{y}\right){}\frac{{\partial }}{{\partial }{y}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}\right]\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{&where}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\left\{\left[\frac{{{\partial }}^{{2}}}{{\partial }{{y}}^{{2}}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{\xi }}{}\left({x}{,}{y}\right){=}{0}{,}\frac{{\partial }}{{\partial }{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{\xi }}{}\left({x}{,}{y}\right){=}{0}{,}\frac{{\partial }}{{\partial }{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{\eta }}{}\left({x}{,}{y}\right){=}{-}\frac{{\partial }}{{\partial }{y}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{\xi }}{}\left({x}{,}{y}\right){,}\frac{{\partial }}{{\partial }{y}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{\eta }}{}\left({x}{,}{y}\right){=}{0}\right]\right\}$ (4)

Compatibility

 • The CleanDependencies command was introduced in Maple 2020.