The CleanDependencies method returns a new LAVF object with any redundant dependant variables or constant of integration removed from its Lie determining system and the corresponding vector field.

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

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

$V≔\mathrm{VectorField}\left(\mathrm{\xi }\left(x\,y\right)\mathrm{D}\left[x\right]+\mathrm{\eta }\left(x\,y\right)\mathrm{D}\left[y\right]\,\mathrm{space}=\left[x\,y\right]\right)$

$V≔\mathrm{\xi }\left(x\,y\right)\left(\frac{\ⅆ}{\ⅆx}\right)+\mathrm{\eta }\left(x\,y\right)\left(\frac{\ⅆ}{\ⅆy}\right)$

$\mathrm{E2}≔\mathrm{LHPDE}\left(\left[\mathrm{diff}\left(\mathrm{\xi }\left(x\,y\right)\,y\,y\right)=0\,\mathrm{diff}\left(\mathrm{\eta }\left(x\,y\right)\,x\right)=-\mathrm{diff}\left(\mathrm{\xi }\left(x\,y\right)\,y\right)\,\mathrm{diff}\left(\mathrm{\eta }\left(x\,y\right)\,y\right)=0\,\mathrm{diff}\left(\mathrm{\xi }\left(x\,y\right)\,x\right)=0\,\mathrm{c1}=0\,\mathrm{c2}=0\right]\,\mathrm{indep}=\left[x\,y\right]\,\mathrm{dep}=\left[\mathrm{\xi }\,\mathrm{\eta }\,\mathrm{c1}\,\mathrm{c2}\right]\right)$

$\mathrm{E2}≔\left[\frac{{\partial }^2}{\partial y^2}\mathrm{\xi }\left(x\,y\right)=0\,\frac{\partial }{\partial x}\mathrm{\eta }\left(x\,y\right)=-\frac{\partial }{\partial y}\mathrm{\xi }\left(x\,y\right)\,\frac{\partial }{\partial y}\mathrm{\eta }\left(x\,y\right)=0\,\frac{\partial }{\partial x}\mathrm{\xi }\left(x\,y\right)=0\,\mathrm{c1}=0\,\mathrm{c2}=0\right],\mathrm{indep}=\left[x\,y\right],\mathrm{dep}=\left[\mathrm{\xi }\left(x\,y\right)\,\mathrm{\eta }\left(x\,y\right)\,\mathrm{c1}\,\mathrm{c2}\right]$

$L≔\mathrm{LAVF}\left(V\,\mathrm{E2}\right)$

$L≔\left[\mathrm{\xi }\left(x\,y\right)\left(\frac{\ⅆ}{\ⅆx}\right)+\mathrm{\eta }\left(x\,y\right)\left(\frac{\ⅆ}{\ⅆy}\right)\right]\&where\left\{\left[\frac{{\partial }^2}{\partial y^2}\mathrm{\xi }\left(x\,y\right)=0\,\frac{\partial }{\partial x}\mathrm{\xi }\left(x\,y\right)=0\,\frac{\partial }{\partial x}\mathrm{\eta }\left(x\,y\right)=-\frac{\partial }{\partial y}\mathrm{\xi }\left(x\,y\right)\,\frac{\partial }{\partial y}\mathrm{\eta }\left(x\,y\right)=0\,\mathrm{c1}=0\,\mathrm{c2}=0\right]\right\}$

$\mathrm{CleanDependencies}\left(L\right)$

$\left[\mathrm{\xi }\left(x\,y\right)\left(\frac{\ⅆ}{\ⅆx}\right)+\mathrm{\eta }\left(x\,y\right)\left(\frac{\ⅆ}{\ⅆy}\right)\right]\&where\left\{\left[\frac{{\partial }^2}{\partial y^2}\mathrm{\xi }\left(x\,y\right)=0\,\frac{\partial }{\partial x}\mathrm{\xi }\left(x\,y\right)=0\,\frac{\partial }{\partial x}\mathrm{\eta }\left(x\,y\right)=-\frac{\partial }{\partial y}\mathrm{\xi }\left(x\,y\right)\,\frac{\partial }{\partial y}\mathrm{\eta }\left(x\,y\right)=0\right]\right\}$

The CleanDependencies command was introduced in Maple 2020.

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