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

 > $\mathrm{with}\left(\mathrm{LieAlgebrasOfVectorFields}\right):$
 > $X≔\mathrm{VectorField}\left(\mathrm{\xi }\left(x,y\right)\mathrm{D}\left[x\right]+\mathrm{\eta }\left(x,y\right)\mathrm{D}\left[y\right],\mathrm{space}=\left[x,y\right]\right)$
 ${X}{≔}{\mathrm{\xi }}{}\left({x}{,}{y}\right){}\left(\frac{{ⅆ}}{{ⅆ}{x}}\right){+}{\mathrm{\eta }}{}\left({x}{,}{y}\right){}\left(\frac{{ⅆ}}{{ⅆ}{y}}\right)$ (1)
 > $\mathrm{\Delta }≔\mathrm{VFPDO}\left(\left[a\left[1\right]\mathrm{diff}\left(\mathrm{\xi }\left(x,y\right),x\right)-a\left[2\right]\mathrm{\xi }\left(x,y\right),\mathrm{diff}\left(\mathrm{\eta }\left(x,y\right),x,x\right)-\left({a\left[1\right]}^{2}+{a\left[2\right]}^{2}\right)\mathrm{\eta }\left(x,y\right)\right],X\right)$
 ${\mathrm{\Delta }}{≔}{X}{↦}\left[{{a}}_{{1}}{\cdot }\left(\frac{{ⅆ}}{{ⅆ}{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{X}{}\left({x}\right)\right){-}{{a}}_{{2}}{\cdot }{X}{}\left({x}\right){,}\frac{{{\partial }}^{{2}}}{{\partial }{{x}}^{{2}}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{X}{}\left({y}\right){+}\left({-}{{a}}_{{1}}^{{2}}{-}{{a}}_{{2}}^{{2}}\right){\cdot }{X}{}\left({y}\right)\right]$ (2)
 > $\mathrm{GetSystemCount}\left(\mathrm{\Delta }\right)$
 ${2}$ (3)
 > $\mathrm{GetSpace}\left(\mathrm{\Delta }\right)$
 $\left[{x}{,}{y}\right]$ (4)

Compatibility

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