GetSystemCount - Maple Help

GetSpace

get the space where a VFPDO is operates on

GetSystemCount

get the number of elements returned by a VFPDO object

 Calling Sequence GetSpace( obj) GetSystemCount( obj)

Parameters

 obj - a VDPDO object

Description

 • An VFPDO object $\mathrm{\Delta }$ is an appliable operator. It takes in a list of linear homogeneous differential expressions and returns as a differential operator on vector field that has same components as the differential expressions.
 • The GetSpace(obj) returns a list of space variables that a VFPDO object is operated on.
 • The GetSystemCount(obj) gives you the number of differential expressions.
 • These methods are associated with the VFPDO object. For more detail, see Overview of the VFPDO object.

Examples

 > $\mathrm{with}\left(\mathrm{LieAlgebrasOfVectorFields}\right):$
 > $X≔\mathrm{VectorField}\left(\mathrm{ξ}\left(x,y\right){\mathrm{D}}_{x}+\mathrm{η}\left(x,y\right){\mathrm{D}}_{y},\mathrm{space}=\left[x,y\right]\right)$
 ${X}{≔}{\mathrm{\xi }}{}\left({x}{,}{y}\right){}\left(\frac{{ⅆ}}{{ⅆ}{x}}\right){+}{\mathrm{\eta }}{}\left({x}{,}{y}\right){}\left(\frac{{ⅆ}}{{ⅆ}{y}}\right)$ (1)
 > $\mathrm{Δ}≔\mathrm{VFPDO}\left(\left[{a}_{1}\left(\frac{\partial }{\partial x}\mathrm{ξ}\left(x,y\right)\right)-{a}_{2}\mathrm{ξ}\left(x,y\right),\frac{{\partial }^{2}}{\partial {x}^{2}}\mathrm{η}\left(x,y\right)-\left({a}_{1}^{2}+{a}_{2}^{2}\right)\mathrm{η}\left(x,y\right)\right],X\right)$
 ${\mathrm{\Delta }}{≔}{X}{→}\left[{{a}}_{{1}}{}\left(\frac{{ⅆ}}{{ⅆ}{x}}{}{X}{}\left({x}\right)\right){-}{{a}}_{{2}}{}{X}{}\left({x}\right){,}\frac{{\partial }}{{\partial }{x}}{}\left(\frac{{\partial }}{{\partial }{x}}{}{X}{}\left({y}\right)\right){+}\left({-}{{a}}_{{1}}^{{2}}{-}{{a}}_{{2}}^{{2}}\right){}{X}{}\left({y}\right)\right]$ (2)
 > $\mathrm{GetSystemCount}\left(\mathrm{Δ}\right)$
 ${2}$ (3)
 > $\mathrm{GetSpace}\left(\mathrm{Δ}\right)$
 $\left[{x}{,}{y}\right]$ (4)

Compatibility

 • The GetSpace and GetSystemCount commands were introduced in Maple 2020.