The IsRifReduced method returns true if a LHPDE object is in rif-reduced form, false otherwise. It returns FAIL if the status is unknown.

Let S be a LHPDE object. The IsTotalDegreeRanking method checks if S is rif-reduced with respect to a total degree ranking (see ranking for more detail). It returns FAIL if S is not in rif-reduced form.

For setting a LHPDEs system as being in a rif-reduced form, see LieAlgebrasOfVectorFields[LHPDE]. And, to rif-reduce a LHPDE object, see the RifReduce method.

These methods are associated with the LHPDE object. For more detail, see Overview of the LHPDE object.

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

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

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

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

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

$S≔\mathrm{RifReduce}\left(S\right)$

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

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

$\mathrm{true}$

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

$\mathrm{true}$

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

$\mathrm{S1}≔\left[{\mathrm{\xi }}_x=0\,\mathrm{\eta }=0\right],\mathrm{indep}=\left[x\,y\right],\mathrm{dep}=\left[\mathrm{\xi }\,\mathrm{\eta }\right]$

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

$\mathrm{FAIL}$

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

$\mathrm{FAIL}$

The IsRifReduced and IsTotalDegreeRanking commands were introduced in Maple 2020.

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