A VectorField object X can act as derivation operator.

A derivation is an operator $X$ such that $X\left(f\+g\right)\=X\left(f\right)\+X\left(g\right)$ and $X\left(\mathrm{fg}\right)\=\mathrm{fX}\left(g\right)\+X\left(f\right)g$

Because it can act as an operator, a VectorField object is of type appliable. See Overview of VectorField Overloaded Builtins for more detail.

When a vector field is acting as an operator, it will distribute itself over indexable types such as Vectors, Matrices, lists, and tables.

This method is associated with the VectorField object. For more detail, see Overview of the VectorField object.

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

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

$X≔x\frac{\partial }{\partial x}+y\frac{\partial }{\partial y}$

$X\left(x^2\right)$

$2x^2$

$X\left(\left[x\,x^2\,x^3\right]\right)$

$\left[x\,2x^2\,3x^3\right]$

$A≔\mathrm{Matrix}\left(\left[\left[x\,y\right]\,\left[x^2\,y^2\right]\right]\right)$

$A≔\left[\begin{array}{cc}x& y\\ x^2& y^2\end{array}\right]$

$X\left(A\right)$

$\left[\begin{array}{cc}x& y\\ 2x^2& 2y^2\end{array}\right]$

The VectorField Object as Derivation Operator command was introduced in Maple 2020.

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