RifReduce - Maple Help

RifReduce

reduce a LHPDEs system to a rif-reduced form

 Calling Sequence RifReduce( obj, vars, opts)

Parameters

 obj - a LHPDE object vars - (optional) list (or list of lists) of main dependent variables opts - (optional) sequence of options to control the behaviour of DEtools[rifsimp]

Description

 • The RifReduce method rif-reduces a LHPDE object. It returns a LHPDE object in a rif-reduced from with respect to a given ranking.
 • This is a front-end to the existing Maple command DEtools[rifsimp].
 • The optional arguments will be passed down to DEtools[rifsimp]. In other words, If S is a LHPDE object then RifReduce(S, vars, opts) is equivalent to DEtools[rifsimp](GetSystem(S), vars, opts).
 • The method is associated with the LHPDE object. For more detail, see Overview of the LHPDE object.

Examples

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

Rif-reduce S with respect to a default ranking: ordered list of dependent variables

 > $\mathrm{Sred}≔\mathrm{RifReduce}\left(S\right)$
 ${\mathrm{Sred}}{≔}\left[{{\mathrm{\xi }}}_{{y}{,}{y}}{=}{0}{,}{{\mathrm{\eta }}}_{{x}}{=}{-}{{\mathrm{\xi }}}_{{y}}{,}{{\mathrm{\xi }}}_{{x}}{=}{0}{,}{{\mathrm{\eta }}}_{{y}}{=}{0}\right]{,}{\mathrm{indep}}{=}\left[{x}{,}{y}\right]{,}{\mathrm{dep}}{=}\left[{\mathrm{\eta }}{,}{\mathrm{\xi }}\right]$ (2)
 > $\mathrm{GetRanking}\left(\mathrm{Sred}\right)$
 $\left[{\mathrm{\eta }}{,}{\mathrm{\xi }}\right]$ (3)

Rif-reduce S with respect to a given ranking

 > $\mathrm{Sred1}≔\mathrm{RifReduce}\left(S,\left[\left[\mathrm{\xi }\right],\left[\mathrm{\eta }\right]\right]\right)$
 ${\mathrm{Sred1}}{≔}\left[{{\mathrm{\xi }}}_{{x}}{=}{0}{,}{{\mathrm{\xi }}}_{{y}}{=}{-}{{\mathrm{\eta }}}_{{x}}{,}{{\mathrm{\eta }}}_{{x}{,}{x}}{=}{0}{,}{{\mathrm{\eta }}}_{{y}}{=}{0}\right]{,}{\mathrm{indep}}{=}\left[{x}{,}{y}\right]{,}{\mathrm{dep}}{=}\left[{\mathrm{\eta }}{,}{\mathrm{\xi }}\right]$ (4)
 > $\mathrm{GetRanking}\left(\mathrm{Sred1}\right)$
 $\left[\left[{\mathrm{\xi }}\right]{,}\left[{\mathrm{\eta }}\right]\right]$ (5)

Compatibility

 • The RifReduce command was introduced in Maple 2020.