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.

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

$\mathrm{Typesetting}:-\mathrm{Settings}\left(\mathrm{userep}=\mathrm{true}\right)$

$\mathrm{false}$

$\mathrm{Typesetting}:-\mathrm{Suppress}\left(\left[\mathrm{\xi }\left(x\,y\right)\,\mathrm{\eta }\left(x\,y\right)\right]\right)$

$S≔\mathrm{LHPDE}\left(\left[\mathrm{diff}\left(\mathrm{\xi }\left(x\,y\right)\,x\right)=0\,\mathrm{diff}\left(\mathrm{\eta }\left(x\,y\right)\,y\right)=0\,\mathrm{diff}\left(\mathrm{\xi }\left(x\,y\right)\,y\right)+\mathrm{diff}\left(\mathrm{\eta }\left(x\,y\right)\,x\right)=0\,\mathrm{diff}\left(\mathrm{\xi }\left(x\,y\right)\,y\,y\right)=0\,\mathrm{diff}\left(\mathrm{\eta }\left(x\,y\right)\,x\,x\right)=0\right]\right)$

$S≔\left[{\mathrm{\xi }}_x=0\,{\mathrm{\eta }}_y=0\,{\mathrm{\xi }}_y+{\mathrm{\eta }}_x=0\,{\mathrm{\xi }}_{y,y}=0\,{\mathrm{\eta }}_{x,x}=0\right],\mathrm{indep}=\left[x\,y\right],\mathrm{dep}=\left[\mathrm{\eta }\,\mathrm{\xi }\right]$

$\mathrm{GetRanking}\left(S\right)$

$\mathrm{FAIL}$

$\mathrm{Sred}≔\mathrm{RifReduce}\left(S\,\left[\mathrm{\xi }\,\mathrm{\eta }\right]\right)$

$\mathrm{Sred}≔\left[{\mathrm{\xi }}_{y,y}=0\,{\mathrm{\xi }}_x=0\,{\mathrm{\eta }}_x=-{\mathrm{\xi }}_y\,{\mathrm{\eta }}_y=0\right],\mathrm{indep}=\left[x\,y\right],\mathrm{dep}=\left[\mathrm{\eta }\,\mathrm{\xi }\right]$

$\mathrm{GetRanking}\left(\mathrm{Sred}\right)$

$\left[\mathrm{\xi }\,\mathrm{\eta }\right]$

$\mathrm{S1}≔\mathrm{LHPDE}\left(\left[\mathrm{diff}\left(\mathrm{\eta }\left(y\right)\,y\right)=0\,\mathrm{diff}\left(\mathrm{\xi }\left(x\right)\,x\right)=0\right]\,\mathrm{dep}=\left[\mathrm{\xi }\,\mathrm{\eta }\right]\,\mathrm{indep}=\left[x\,y\right]\,\mathrm{inRifReducedForm}=\mathrm{true}\,\mathrm{ranking}=\left[\mathrm{\eta }\,\mathrm{\xi }\right]\right)$

$\mathrm{S1}≔\left[\frac{\ⅆ}{\ⅆy}\mathrm{\eta }\left(y\right)=0\,\frac{\ⅆ}{\ⅆx}\mathrm{\xi }\left(x\right)=0\right],\mathrm{indep}=\left[x\,y\right],\mathrm{dep}=\left[\mathrm{\xi }\left(x\right)\,\mathrm{\eta }\left(y\right)\right]$

$\mathrm{GetRanking}\left(\mathrm{S1}\right)$

$\left[\mathrm{\eta }\,\mathrm{\xi }\right]$

The GetRanking command was introduced in Maple 2020.

For more information on Maple 2020 changes, see Updates in Maple 2020.