An LHPDO object $\mathrm{\Delta }$ is an appliable operator. If it acts on a list containing $m$ elements and returns a list containing $s$ elements, then GetDependentsCount(Delta) returns $m$ and GetSystemCount(Delta) returns  $s$.

The $m$ elements acted on by LHPDO Delta may have dependency restrictions.  These restrictions can be retrieved by the call GetDependencies(Delta).

These methods are associated with the LHPDO object. For more detail, see Overview of the LHPDO object.

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

$\mathrm{\Delta }≔\mathrm{LHPDO}\left(\left[\mathrm{diff}\left(\mathrm{\xi }\left(x\,y\right)\,y\,y\right)=0\,\mathrm{diff}\left(\mathrm{\eta }\left(x\,y\right)\,x\right)=-\mathrm{diff}\left(\mathrm{\xi }\left(x\,y\right)\,y\right)\,\mathrm{diff}\left(\mathrm{\eta }\left(x\,y\right)\,y\right)=0\,\mathrm{diff}\left(\mathrm{\xi }\left(x\,y\right)\,x\right)=0\right]\right)$

$\mathrm{\Delta }≔\left(\mathrm{\η}\,\mathrm{\ξ}\right)\→\left[\frac{\partial }{\partial y}\left(\frac{\partial }{\partial y}\mathrm{\ξ}\right)\,\frac{\partial }{\partial x}\mathrm{\η}\+\frac{\partial }{\partial y}\mathrm{\ξ}\,\frac{\partial }{\partial y}\mathrm{\η}\,\frac{\partial }{\partial x}\mathrm{\ξ}\right]$

$\mathrm{GetDependentsCount}\left(\mathrm{\Delta }\right)$

$2$

$\mathrm{GetSystemCount}\left(\mathrm{\Delta }\right)$

$4$

$\mathrm{GetDependencies}\left(\mathrm{\Delta }\right)$

$\left[\left[x\,y\right]\,\left[x\,y\right]\right]$

$Q≔\mathrm{LHPDO}\left(\left[\mathrm{diff}\left(u\left(x\right)\,x\,x\right)-u\left(x\right)\,\mathrm{diff}\left(v\left(y\right)\,y\,y\right)\right]\right)$

$Q≔\left(u\,v\right)\→\left[\frac{\partial }{\partial x}\left(\frac{\partial }{\partial x}u\right)-u\,\frac{\partial }{\partial y}\left(\frac{\partial }{\partial y}v\right)\right]$

$\mathrm{GetDependentsCount}\left(Q\right)$

$2$

$\mathrm{GetDependencies}\left(Q\right)$

$\left[\left[x\right]\,\left[y\right]\right]$

The GetDependentsCount, GetDependencies and GetSystemCount commands were introduced in Maple 2020.

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