 GetDependentsCount - Maple Help

GetDependentsCount

get the number of elements that a LHPDO object operates on

GetDependencies

get the dependencies of elements that a LHPDO object may operate on

GetSystemCount

get the number of elements returned by a LHPDO object Calling Sequence GetDependentsCount( obj) GetDependencies( obj) GetSystemCount( obj) Parameters

 obj - a LHPDO object Description

 • 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. Examples

 > $\mathrm{with}\left(\mathrm{LieAlgebrasOfVectorFields}\right):$
 > $\mathrm{Δ}≔\mathrm{LHPDO}\left(\left[\frac{{\partial }^{2}}{\partial {y}^{2}}\mathrm{ξ}\left(x,y\right)=0,\frac{\partial }{\partial x}\mathrm{η}\left(x,y\right)=-\left(\frac{\partial }{\partial y}\mathrm{ξ}\left(x,y\right)\right),\frac{\partial }{\partial y}\mathrm{η}\left(x,y\right)=0,\frac{\partial }{\partial x}\mathrm{ξ}\left(x,y\right)=0\right]\right)$
 ${\mathrm{\Delta }}{≔}\left({\mathrm{η}}{,}{\mathrm{ξ}}\right){→}\left[\frac{{\partial }}{{\partial }{y}}{}\left(\frac{{\partial }}{{\partial }{y}}{}{\mathrm{ξ}}\right){,}\frac{{\partial }}{{\partial }{x}}{}{\mathrm{η}}{+}\frac{{\partial }}{{\partial }{y}}{}{\mathrm{ξ}}{,}\frac{{\partial }}{{\partial }{y}}{}{\mathrm{η}}{,}\frac{{\partial }}{{\partial }{x}}{}{\mathrm{ξ}}\right]$ (1)

The operator Delta takes in a list of 2 elements and returns a list of 4 elements...

 > $\mathrm{GetDependentsCount}\left(\mathrm{Δ}\right)$
 ${2}$ (2)
 > $\mathrm{GetSystemCount}\left(\mathrm{Δ}\right)$
 ${4}$ (3)

The arguments of Delta here may both depend on (x,y) ...

 > $\mathrm{GetDependencies}\left(\mathrm{Δ}\right)$
 $\left[\left[{x}{,}{y}\right]{,}\left[{x}{,}{y}\right]\right]$ (4)
 > $Q≔\mathrm{LHPDO}\left(\left[\frac{{ⅆ}^{2}}{ⅆ{x}^{2}}u\left(x\right)-u\left(x\right),\frac{{ⅆ}^{2}}{ⅆ{y}^{2}}v\left(y\right)\right]\right)$
 ${Q}{≔}\left({u}{,}{v}\right){→}\left[\frac{{\partial }}{{\partial }{x}}{}\left(\frac{{\partial }}{{\partial }{x}}{}{u}\right){-}{u}{,}\frac{{\partial }}{{\partial }{y}}{}\left(\frac{{\partial }}{{\partial }{y}}{}{v}\right)\right]$ (5)

The operator Q acts on a list of 2 elements, say [u,v]...

 > $\mathrm{GetDependentsCount}\left(Q\right)$
 ${2}$ (6)

The first list item u may depend on x only, the second item v may depend on y only...

 > $\mathrm{GetDependencies}\left(Q\right)$
 $\left[\left[{x}\right]{,}\left[{y}\right]\right]$ (7) Compatibility

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