The GetSpace method returns a list of space coordinate variables where the LAVF, Distribution, or VFPDO object lives.

To be more specific, the space where these object live is the space where their vector fields live. For example, let L be a LAVF object, then the call GetSpace(L) is equivalent to GetSpace(GetVectorField(L)). See GetSpace of a VectorField object for more detail.

This method is associated with the LAVF, Distribution, and VFPDO objects. For more detail, see Overview of the LAVF object, overview of the Distribution object, and overview of the VFPDO object.

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

$\mathrm{Typesetting}:-\mathrm{Settings}\left(\mathrm{userep}=\mathrm{true}\right)\:$

$\mathrm{Typesetting}:-\mathrm{Suppress}\left(\left[\mathrm{\xi }\left(x\,y\right)\,\mathrm{\eta }\left(x\,y\right)\right]\right)\:$

$V≔\mathrm{VectorField}\left(\mathrm{\xi }\left(x\,y\right)\mathrm{D}\left[x\right]+\mathrm{\eta }\left(x\,y\right)\mathrm{D}\left[y\right]\,\mathrm{space}=\left[x\,y\right]\right)$

$V≔\mathrm{\xi }\left(\frac{\ⅆ}{\ⅆx}\right)+\mathrm{\eta }\left(\frac{\ⅆ}{\ⅆy}\right)$

$\mathrm{E2}≔\mathrm{LHPDE}\left(\left[\mathrm{diff}\left(\mathrm{\xi }\left(x\,y\right)\,y\,y\right)=0\,\mathrm{diff}\left(\mathrm{\eta }\left(x\,y\right)\,x\right)=-\mathrm{diff}\left(\mathrm{\xi }\left(x\,y\right)\,y\right)\,\mathrm{diff}\left(\mathrm{\eta }\left(x\,y\right)\,y\right)=0\,\mathrm{diff}\left(\mathrm{\xi }\left(x\,y\right)\,x\right)=0\right]\,\mathrm{indep}=\left[x\,y\right]\,\mathrm{dep}=\left[\mathrm{\xi }\,\mathrm{\eta }\right]\right)$

$\mathrm{E2}≔\left[{\mathrm{\xi }}_{y,y}=0\,{\mathrm{\eta }}_x=-{\mathrm{\xi }}_y\,{\mathrm{\eta }}_y=0\,{\mathrm{\xi }}_x=0\right],\mathrm{indep}=\left[x\,y\right],\mathrm{dep}=\left[\mathrm{\xi }\,\mathrm{\eta }\right]$

$L≔\mathrm{LAVF}\left(V\,\mathrm{E2}\right)$

$L≔\left[\mathrm{\xi }\left(\frac{\ⅆ}{\ⅆx}\right)+\mathrm{\eta }\left(\frac{\ⅆ}{\ⅆy}\right)\right]\&where\left\{\left[{\mathrm{\xi }}_{y,y}=0\,{\mathrm{\xi }}_x=0\,{\mathrm{\eta }}_x=-{\mathrm{\xi }}_y\,{\mathrm{\eta }}_y=0\right]\right\}$

$\mathrm{GetSpace}\left(L\right)$

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

$\mathrm{OD}≔\mathrm{OrbitDistribution}\left(L\right)$

$\mathrm{OD}≔\left\{\frac{\ⅆ}{\ⅆy}\,\frac{\ⅆ}{\ⅆx}\right\}$

$\mathrm{GetSpace}\left(\mathrm{OD}\right)$

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

$\mathrm{\Delta }≔\mathrm{VFPDO}\left(L\right)$

$\mathrm{\Delta }≔X\mapsto \left[\frac{{\partial }^2}{\partial y^2}X\left(x\right)\,\frac{\ⅆ}{\ⅆx}X\left(x\right)\,\frac{\partial }{\partial x}X\left(y\right)+\frac{\partial }{\partial y}X\left(x\right)\,\frac{\ⅆ}{\ⅆy}X\left(y\right)\right]$

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

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

The GetSpace command was introduced in Maple 2020.

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