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.

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

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

$X≔\mathrm{\xi }\left(x\,y\right)\left(\frac{\ⅆ}{\ⅆx}\right)+\mathrm{\eta }\left(x\,y\right)\left(\frac{\ⅆ}{\ⅆy}\right)$

$\mathrm{\Delta }≔\mathrm{VFPDO}\left(\left[a\left[1\right]\mathrm{diff}\left(\mathrm{\xi }\left(x\,y\right)\,x\right)-a\left[2\right]\mathrm{\xi }\left(x\,y\right)\,\mathrm{diff}\left(\mathrm{\eta }\left(x\,y\right)\,x\,x\right)-\left({a\left[1\right]}^2+{a\left[2\right]}^2\right)\mathrm{\eta }\left(x\,y\right)\right]\,X\right)$

$\mathrm{\Delta }≔X\mapsto \left[a_1\cdot \left(\frac{\ⅆ}{\ⅆx}X\left(x\right)\right)-a_2\cdot X\left(x\right)\,\frac{{\partial }^2}{\partial x^2}X\left(y\right)+\left(-a_1^2-a_2^2\right)\cdot X\left(y\right)\right]$

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

$2$

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

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

The GetSpace and GetSystemCount commands were introduced in Maple 2020.

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