GetRanking - Maple Help

GetRanking

get ranking of a rif-reduced LHPDEs system

 Calling Sequence GetRanking( obj)

Parameters

 obj - a LHPDE object that is in rif-reduced form.

Description

 • For a LHPDE object that is in rif-reduced form, the GetRanking method returns the ranking of the LHPDE object as a list (or a list of lists) of dependent variable names, if available.
 • The method returns FAIL if the ranking is unavailable or a LHPDE object is not recorded as being in rif-reduced form.
 • The returned output - ranking of a LHPDE object - is consistent with the ranking that is used on the DEtools[rifsimp] command. See ranking for more detail.
 • Rif reduction refers to the differential reduction and completion algorithm performed by the Maple command DEtools[rifsimp].
 • To rif-reduce a LHPDE object with specific ranking, see RifReduce for more detail.
 • The ranking can be set while constructing a LHPDE object. See LieAlgebrasOfVectorFields[LHPDE] for more detail.
 • This method is associated with the LHPDE object. For more detail, see Overview of the LHPDE object.

Examples

 > $\mathrm{with}\left(\mathrm{LieAlgebrasOfVectorFields}\right):$
 > $\mathrm{Typesetting}:-\mathrm{Settings}\left(\mathrm{userep}=\mathrm{true}\right)$
 ${\mathrm{false}}$ (1)
 > $\mathrm{Typesetting}:-\mathrm{Suppress}\left(\left[\mathrm{\xi }\left(x,y\right),\mathrm{\eta }\left(x,y\right)\right]\right)$
 > $S≔\mathrm{LHPDE}\left(\left[\mathrm{diff}\left(\mathrm{\xi }\left(x,y\right),x\right)=0,\mathrm{diff}\left(\mathrm{\eta }\left(x,y\right),y\right)=0,\mathrm{diff}\left(\mathrm{\xi }\left(x,y\right),y\right)+\mathrm{diff}\left(\mathrm{\eta }\left(x,y\right),x\right)=0,\mathrm{diff}\left(\mathrm{\xi }\left(x,y\right),y,y\right)=0,\mathrm{diff}\left(\mathrm{\eta }\left(x,y\right),x,x\right)=0\right]\right)$
 ${S}{≔}\left[{{\mathrm{\xi }}}_{{x}}{=}{0}{,}{{\mathrm{\eta }}}_{{y}}{=}{0}{,}{{\mathrm{\xi }}}_{{y}}{+}{{\mathrm{\eta }}}_{{x}}{=}{0}{,}{{\mathrm{\xi }}}_{{y}{,}{y}}{=}{0}{,}{{\mathrm{\eta }}}_{{x}{,}{x}}{=}{0}\right]{,}{\mathrm{indep}}{=}\left[{x}{,}{y}\right]{,}{\mathrm{dep}}{=}\left[{\mathrm{\eta }}{,}{\mathrm{\xi }}\right]$ (2)
 > $\mathrm{GetRanking}\left(S\right)$
 ${\mathrm{FAIL}}$ (3)

Using the RifReduce method to reduce a LHPDE object with given ranking:

 > $\mathrm{Sred}≔\mathrm{RifReduce}\left(S,\left[\mathrm{\xi },\mathrm{\eta }\right]\right)$
 ${\mathrm{Sred}}{≔}\left[{{\mathrm{\xi }}}_{{y}{,}{y}}{=}{0}{,}{{\mathrm{\xi }}}_{{x}}{=}{0}{,}{{\mathrm{\eta }}}_{{x}}{=}{-}{{\mathrm{\xi }}}_{{y}}{,}{{\mathrm{\eta }}}_{{y}}{=}{0}\right]{,}{\mathrm{indep}}{=}\left[{x}{,}{y}\right]{,}{\mathrm{dep}}{=}\left[{\mathrm{\eta }}{,}{\mathrm{\xi }}\right]$ (4)
 > $\mathrm{GetRanking}\left(\mathrm{Sred}\right)$
 $\left[{\mathrm{\xi }}{,}{\mathrm{\eta }}\right]$ (5)

Specify ranking while constructing a LHPDE object:

 > $\mathrm{S1}≔\mathrm{LHPDE}\left(\left[\mathrm{diff}\left(\mathrm{\eta }\left(y\right),y\right)=0,\mathrm{diff}\left(\mathrm{\xi }\left(x\right),x\right)=0\right],\mathrm{dep}=\left[\mathrm{\xi },\mathrm{\eta }\right],\mathrm{indep}=\left[x,y\right],\mathrm{inRifReducedForm}=\mathrm{true},\mathrm{ranking}=\left[\mathrm{\eta },\mathrm{\xi }\right]\right)$
 ${\mathrm{S1}}{≔}\left[\frac{{ⅆ}}{{ⅆ}{y}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{\eta }}{}\left({y}\right){=}{0}{,}\frac{{ⅆ}}{{ⅆ}{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{\mathrm{\xi }}{}\left({x}\right){=}{0}\right]{,}{\mathrm{indep}}{=}\left[{x}{,}{y}\right]{,}{\mathrm{dep}}{=}\left[{\mathrm{\xi }}{}\left({x}\right){,}{\mathrm{\eta }}{}\left({y}\right)\right]$ (6)
 > $\mathrm{GetRanking}\left(\mathrm{S1}\right)$
 $\left[{\mathrm{\eta }}{,}{\mathrm{\xi }}\right]$ (7)

Compatibility

 • The GetRanking command was introduced in Maple 2020.