GetSpace - Maple Programming Help

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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

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

Compatibility

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