The evalVF(F, v) calling sequence evaluates the vector field F at the point v.  The parameters, F and v, must have the same dimension, but do not need to be defined in the same coordinate system.

The vector field parameter, F, can also be specified as a Vector-valued procedure, in which case this procedure is evaluated at the coordinates of the Vector v.

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{VectorCalculus}\right]\right)\:$

$\mathrm{SetCoordinates}\left(\mathrm{polar}\left[r,\mathrm{\theta }\right]\right)$

${\mathrm{polar}}_{r,\mathrm{\theta }}$

$F≔\mathrm{VectorField}\left(⟨r^2\mathrm{\theta }\,-\mathrm{\theta }⟩\right)$

$F≔\left(r^2\mathrm{\theta }\right){\stackrel{\_}{e}}_r\+\left(-\mathrm{\theta }\right){\stackrel{\_}{e}}_{\mathrm{\θ}}$

$\mathrm{simplify}\left(\mathrm{evalVF}\left(F\,⟨1\,\frac{\mathrm{\pi }}{2}⟩\right)\right)$

$\left[\begin{array}{c}\frac{\mathrm{\pi }}{2}\\ -\frac{\mathrm{\pi }}{2}\end{array}\right]$

$\mathrm{evalVF}\left(\left(a\,b\right)\mapsto ⟨a^2\,b^2⟩\,\mathrm{Vector}\left(\left[0\,1\right]\,\mathrm{attributes}=\left[\mathrm{coordinates}=\mathrm{cartesian}\right]\right)\right)$

$\left[\begin{array}{c}1\\ \frac{{\mathrm{\pi }}^2}{4}\end{array}\right]$