IsRifReduced - Maple Help

IsRifReduced

check if a LHPDEs system is in rif-reduced form

IsTotalDegreeRanking

check if a LHPDEs system is rif-reduced with respect to a total degree ranking

 Calling Sequence IsRifReduced( obj) IsTotalDegreeRanking( obj)

Parameters

 obj - a LHPDE object

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{LieAlgebrasOfVectorFields}\right):$
 > $\mathrm{Typesetting}:-\mathrm{Suppress}\left(\left[\mathrm{\xi }\left(x,y\right),\mathrm{\eta }\left(x,y\right)\right]\right):$
 > $\mathrm{Typesetting}:-\mathrm{Settings}\left(\mathrm{userep}=\mathrm{true}\right):$
 > $S≔\mathrm{LHPDE}\left(\left[\mathrm{diff}\left(\mathrm{\xi }\left(x,y\right),y,y\right)=0,\mathrm{diff}\left(\mathrm{\eta }\left(x,y\right),x\right)+\mathrm{diff}\left(\mathrm{\xi }\left(x,y\right),y\right)=0,\mathrm{diff}\left(\mathrm{\eta }\left(x,y\right),y\right)=0,\mathrm{diff}\left(\mathrm{\xi }\left(x,y\right),x\right)=0,\mathrm{diff}\left(\mathrm{\eta }\left(x,y\right),x,x\right)=0\right],\mathrm{indep}=\left[x,y\right],\mathrm{dep}=\left[\mathrm{\xi },\mathrm{\eta }\right]\right)$
 ${S}{≔}\left[{{\mathrm{\xi }}}_{{y}{,}{y}}{=}{0}{,}{{\mathrm{\eta }}}_{{x}}{+}{{\mathrm{\xi }}}_{{y}}{=}{0}{,}{{\mathrm{\eta }}}_{{y}}{=}{0}{,}{{\mathrm{\xi }}}_{{x}}{=}{0}{,}{{\mathrm{\eta }}}_{{x}{,}{x}}{=}{0}\right]{,}{\mathrm{indep}}{=}\left[{x}{,}{y}\right]{,}{\mathrm{dep}}{=}\left[{\mathrm{\xi }}{,}{\mathrm{\eta }}\right]$ (1)
 > $S≔\mathrm{RifReduce}\left(S\right)$
 ${S}{≔}\left[{{\mathrm{\xi }}}_{{y}{,}{y}}{=}{0}{,}{{\mathrm{\xi }}}_{{x}}{=}{0}{,}{{\mathrm{\eta }}}_{{x}}{=}{-}{{\mathrm{\xi }}}_{{y}}{,}{{\mathrm{\eta }}}_{{y}}{=}{0}\right]{,}{\mathrm{indep}}{=}\left[{x}{,}{y}\right]{,}{\mathrm{dep}}{=}\left[{\mathrm{\xi }}{,}{\mathrm{\eta }}\right]$ (2)
 > $\mathrm{IsRifReduced}\left(S\right)$
 ${\mathrm{true}}$ (3)
 > $\mathrm{IsTotalDegreeRanking}\left(S\right)$
 ${\mathrm{true}}$ (4)

The status of S1 for being a rif-reduced form is not known:

 > $\mathrm{S1}≔\mathrm{LHPDE}\left(\left[\mathrm{diff}\left(\mathrm{\xi }\left(x,y\right),x\right)=0,\mathrm{\eta }\left(x,y\right)=0\right],\mathrm{indep}=\left[x,y\right],\mathrm{dep}=\left[\mathrm{\xi },\mathrm{\eta }\right]\right)$
 ${\mathrm{S1}}{≔}\left[{{\mathrm{\xi }}}_{{x}}{=}{0}{,}{\mathrm{\eta }}{=}{0}\right]{,}{\mathrm{indep}}{=}\left[{x}{,}{y}\right]{,}{\mathrm{dep}}{=}\left[{\mathrm{\xi }}{,}{\mathrm{\eta }}\right]$ (5)

Therefore, information will not be available..

 > $\mathrm{IsRifReduced}\left(\mathrm{S1}\right)$
 ${\mathrm{FAIL}}$ (6)
 > $\mathrm{IsTotalDegreeRanking}\left(\mathrm{S1}\right)$
 ${\mathrm{FAIL}}$ (7)

Compatibility

 • The IsRifReduced and IsTotalDegreeRanking commands were introduced in Maple 2020.