GetRanking - Maple Help
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GetRanking

get ranking of the rif-reduced symmetry determining system

 Calling Sequence GetRanking( obj)

Parameters

 obj - a LAVF object that its symmetry determinings system is in rif-reduced form.

Description

 • For a LAVF object, the GetRanking method returns the ranking of the rif-reduced symmetry determining system as a list (or a list of lists) of dependent variable names, if available.
 • This method is front-end to the GetRanking method of a LHPDE object. That is, let S be the determining systems of LAVF objects L then GetRanking(L) equals GetRanking(S).
 • The returned output - ranking of a LAVF object - is consistent with the ranking that is used on the DEtools[rifsimp] command. See ranking for more detail.
 • This method is associated with the LAVF object. For more detail, see Overview of the LAVF object.

Examples

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

Construct an LAVF object...

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

Compatibility

 • The GetRanking command was introduced in Maple 2020.
 • For more information on Maple 2020 changes, see Updates in Maple 2020.