GetRanking - Maple Programming Help

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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

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

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

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

Specify ranking while constructing a LHPDE object:

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

Compatibility

 • The GetRanking command was introduced in Maple 2020.