The ReducedForm method reduces a list (or set) of differential expressions modulo a rif-reduced LHPDE object. It returns the reduced form as a list (or set) of differential expressions.

Essentially the method substitutes the LHPDE equations into the differential expressions expr, until no more substitutions can be done.

To perform the reduction, the method ultimately calls a version of the Maple command dsubs.

This method is associated with the LHPDE object. For more detail, see Overview of the LHPDE object.

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

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

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

$\mathrm{E2}≔\mathrm{LHPDE}\left(\left[\mathrm{diff}\left(\mathrm{\xi }\left(x\,y\right)\,y\,y\right)=0\,\mathrm{diff}\left(\mathrm{\eta }\left(x\,y\right)\,x\right)=-\mathrm{diff}\left(\mathrm{\xi }\left(x\,y\right)\,y\right)\,\mathrm{diff}\left(\mathrm{\eta }\left(x\,y\right)\,y\right)=0\,\mathrm{diff}\left(\mathrm{\xi }\left(x\,y\right)\,x\right)=0\right]\,\mathrm{indep}=\left[x\,y\right]\,\mathrm{dep}=\left[\mathrm{\xi }\,\mathrm{\eta }\right]\right)$

$\mathrm{E2}≔\left[{\mathrm{\xi }}_{y,y}=0\,{\mathrm{\eta }}_x=-{\mathrm{\xi }}_y\,{\mathrm{\eta }}_y=0\,{\mathrm{\xi }}_x=0\right],\mathrm{indep}=\left[x\,y\right],\mathrm{dep}=\left[\mathrm{\xi }\,\mathrm{\eta }\right]$

$\mathrm{expr}≔\left[\mathrm{diff}\left(\mathrm{\xi }\left(x\,y\right)\,x\,y\right)\,\mathrm{diff}\left(\mathrm{\eta }\left(x\,y\right)\,x\,x\right)\,\mathrm{diff}\left(\mathrm{\xi }\left(x\,y\right)\,y\right)\,\mathrm{diff}\left(\mathrm{\eta }\left(x\,y\right)\,x\right)+\mathrm{diff}\left(\mathrm{\eta }\left(x\,y\right)\,y\right)\right]$

$\mathrm{expr}≔\left[{\mathrm{\xi }}_{x,y}\,{\mathrm{\eta }}_{x,x}\,{\mathrm{\xi }}_y\,{\mathrm{\eta }}_x+{\mathrm{\eta }}_y\right]$

$\mathrm{ReducedForm}\left(\mathrm{expr}\,\mathrm{E2}\right)$

$\left[0\,0\,{\mathrm{\xi }}_y\,-{\mathrm{\xi }}_y\right]$

$\mathrm{ReducedForm}\left(\mathrm{convert}\left(\mathrm{expr}\,'\mathrm{set}'\right)\,\mathrm{E2}\right)$

$\left\{0\,-{\mathrm{\xi }}_y\,{\mathrm{\xi }}_y\right\}$

The ReducedForm command was introduced in Maple 2020.

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