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.

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

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

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

$S≔\mathrm{LHPDE}\left(\left[\frac{\partial }{\partial x}\mathrm{\ξ}\left(x\,y\right)\=0\,\frac{\partial }{\partial y}\mathrm{\η}\left(x\,y\right)\=0\,\frac{\partial }{\partial y}\mathrm{\ξ}\left(x\,y\right)\+\frac{\partial }{\partial x}\mathrm{\η}\left(x\,y\right)\=0\,\frac{{\partial }^2}{\partial y^2}\mathrm{\ξ}\left(x\,y\right)\=0\,\frac{{\partial }^2}{\partial x^2}\mathrm{\η}\left(x\,y\right)\=0\right]\right)$

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

$\mathrm{Sred}≔\mathrm{RifReduce}\left(S\right)$

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

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

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

$\mathrm{Sred1}≔\mathrm{RifReduce}\left(S\,\left[\left[\mathrm{\ξ}\right]\,\left[\mathrm{\η}\right]\right]\right)$

$\mathrm{Sred1}≔\left[{\mathrm{\xi }}_x=0\,{\mathrm{\xi }}_y=-{\mathrm{\eta }}_x\,{\mathrm{\eta }}_{x,x}=0\,{\mathrm{\eta }}_y=0\right],\mathrm{indep}=\left[x\,y\right],\mathrm{dep}=\left[\mathrm{\eta }\,\mathrm{\xi }\right]$

$\mathrm{GetRanking}\left(\mathrm{Sred1}\right)$

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

The RifReduce command was introduced in Maple 2020.

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