GetIndependents - Maple Help

GetIndependents

get independent variables of a LHPDE or LHPDO object

 Calling Sequence GetIndependents( obj)

Parameters

 obj - a LHPDE or LHPDO object.

Description

 • The GetIndependents method returns a list of independent variables for a LHPDE or LHPDO object.
 • This method is associated with the LHPDE and LHPDO objects. For more detail, see Overview of the LHPDE object and Overview of the LHPDO object.

Examples

 > $\mathrm{with}\left(\mathrm{LieAlgebrasOfVectorFields}\right):$
 > $S≔\mathrm{LHPDE}\left(\left[\frac{{\partial }^{2}}{\partial {x}^{2}}u\left(x,y\right)-\left(\frac{{\partial }^{2}}{\partial {y}^{2}}v\left(x,y\right)\right)=0\right]\right)$
 ${S}{≔}\left[\frac{{{\partial }}^{{2}}}{{\partial }{{x}}^{{2}}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{u}{}\left({x}{,}{y}\right){-}\frac{{{\partial }}^{{2}}}{{\partial }{{y}}^{{2}}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{v}{}\left({x}{,}{y}\right){=}{0}\right]{,}{\mathrm{indep}}{=}\left[{x}{,}{y}\right]{,}{\mathrm{dep}}{=}\left[{u}{}\left({x}{,}{y}\right){,}{v}{}\left({x}{,}{y}\right)\right]$ (1)
 > $\mathrm{GetIndependents}\left(S\right)$
 $\left[{x}{,}{y}\right]$ (2)
 > $\mathrm{Δ}≔\mathrm{LHPDO}\left(S\right)$
 ${\mathrm{\Delta }}{≔}\left({u}{,}{v}\right){→}\left[\frac{{\partial }}{{\partial }{x}}{}\left(\frac{{\partial }}{{\partial }{x}}{}{u}\right){-}\left(\frac{{\partial }}{{\partial }{y}}{}\left(\frac{{\partial }}{{\partial }{y}}{}{v}\right)\right)\right]$ (3)
 > $\mathrm{GetIndependents}\left(\mathrm{Δ}\right)$
 $\left[{x}{,}{y}\right]$ (4)

Compatibility

 • The GetIndependents command was introduced in Maple 2020.