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ReducedForm

compute reduced form of differential expressions modulo a LHPDE

 Calling Sequence ReducedForm(expr, obj)

Parameters

 expr - a list or set of differential expressions obj - a rif-reduced LHPDE object (see IsRifReduced)

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{LieAlgebrasOfVectorFields}\right):$
 > $\mathrm{Typesetting}:-\mathrm{Settings}\left(\mathrm{userep}=\mathrm{true}\right):$
 > $\mathrm{Typesetting}:-\mathrm{Suppress}\left(\left[\mathrm{\xi }\left(x,y\right),\mathrm{\eta }\left(x,y\right)\right]\right)$
 > $\mathrm{E2}≔\mathrm{LHPDE}\left(\left[\mathrm{diff}\left(\mathrm{\xi }\left(x,y\right),y,y\right)=0,\mathrm{diff}\left(\mathrm{\eta }\left(x,y\right),x\right)=-\mathrm{diff}\left(\mathrm{\xi }\left(x,y\right),y\right),\mathrm{diff}\left(\mathrm{\eta }\left(x,y\right),y\right)=0,\mathrm{diff}\left(\mathrm{\xi }\left(x,y\right),x\right)=0\right],\mathrm{indep}=\left[x,y\right],\mathrm{dep}=\left[\mathrm{\xi },\mathrm{\eta }\right]\right)$
 ${\mathrm{E2}}{≔}\left[{{\mathrm{\xi }}}_{{y}{,}{y}}{=}{0}{,}{{\mathrm{\eta }}}_{{x}}{=}{-}{{\mathrm{\xi }}}_{{y}}{,}{{\mathrm{\eta }}}_{{y}}{=}{0}{,}{{\mathrm{\xi }}}_{{x}}{=}{0}\right]{,}{\mathrm{indep}}{=}\left[{x}{,}{y}\right]{,}{\mathrm{dep}}{=}\left[{\mathrm{\xi }}{,}{\mathrm{\eta }}\right]$ (1)
 > $\mathrm{expr}≔\left[\mathrm{diff}\left(\mathrm{\xi }\left(x,y\right),x,y\right),\mathrm{diff}\left(\mathrm{\eta }\left(x,y\right),x,x\right),\mathrm{diff}\left(\mathrm{\xi }\left(x,y\right),y\right),\mathrm{diff}\left(\mathrm{\eta }\left(x,y\right),x\right)+\mathrm{diff}\left(\mathrm{\eta }\left(x,y\right),y\right)\right]$
 ${\mathrm{expr}}{≔}\left[{{\mathrm{\xi }}}_{{x}{,}{y}}{,}{{\mathrm{\eta }}}_{{x}{,}{x}}{,}{{\mathrm{\xi }}}_{{y}}{,}{{\mathrm{\eta }}}_{{x}}{+}{{\mathrm{\eta }}}_{{y}}\right]$ (2)
 > $\mathrm{ReducedForm}\left(\mathrm{expr},\mathrm{E2}\right)$
 $\left[{0}{,}{0}{,}{{\mathrm{\xi }}}_{{y}}{,}{-}{{\mathrm{\xi }}}_{{y}}\right]$ (3)
 > $\mathrm{ReducedForm}\left(\mathrm{convert}\left(\mathrm{expr},'\mathrm{set}'\right),\mathrm{E2}\right)$
 $\left\{{0}{,}{-}{{\mathrm{\xi }}}_{{y}}{,}{{\mathrm{\xi }}}_{{y}}\right\}$ (4)

Compatibility

 • The ReducedForm command was introduced in Maple 2020.