The About(v) command returns the type and all relevant data of a VectorCalculus object in a human-readable format.

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

$\mathrm{vs}≔\mathrm{VectorSpace}\left(\mathrm{polar}\left[r,\mathrm{\theta }\right]\,⟨0\,1⟩\right)\:$

$\mathrm{About}\left(\mathrm{vs}\right)$

$\left[\begin{array}{cc}\mathrm{Type:}& \mathrm{Vector\; Space}\\ \mathrm{Coordinates:}& {\mathrm{polar}}_{r,\mathrm{\theta }}\\ \mathrm{Root\; Point:}& \left[1\,\frac{\mathrm{\pi }}{2}\right]\end{array}\right]$

$\mathrm{rv}≔\mathrm{vs}:-\mathrm{Vector}\left(\left[1\,1\right]\right)\:$

$\mathrm{About}\left(\mathrm{rv}\right)$

$\left[\begin{array}{cc}\mathrm{Type:}& \mathrm{Rooted\; Vector}\\ \mathrm{Components:}& \left[1\,1\right]\\ \mathrm{Coordinates:}& {\mathrm{polar}}_{r,\mathrm{\theta }}\\ \mathrm{Root\; Point:}& \left[1\,\frac{\mathrm{\pi }}{2}\right]\end{array}\right]$

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

${\mathrm{spherical}}_{r,\mathrm{\phi },\mathrm{\theta }}$

$\mathrm{fv}≔⟨1\,\frac{\mathrm{\pi }}{2}\,\mathrm{\pi }⟩\:$

$\mathrm{About}\left(\mathrm{fv}\right)$

$\left[\begin{array}{cc}\mathrm{Type:}& \mathrm{Free\; Vector}\\ \mathrm{Components:}& \left[1\,\frac{\mathrm{\pi }}{2}\,\mathrm{\pi }\right]\\ \mathrm{Coordinates:}& {\mathrm{spherical}}_{r,\mathrm{\phi },\mathrm{\theta }}\end{array}\right]$

$\mathrm{SetCoordinates}\left(\mathrm{cartesian}\left[x,y\right]\right)$

${\mathrm{cartesian}}_{x,y}$

$\mathrm{vf}≔\mathrm{VectorField}\left(⟨y\,xy⟩\right)\:$

$\mathrm{About}\left(\mathrm{vf}\right)$

$\left[\begin{array}{cc}\mathrm{Type:}& \mathrm{Vector\; Field}\\ \mathrm{Components:}& \left[y\,xy\right]\\ \mathrm{Coordinates:}& {\mathrm{cartesian}}_{x,y}\end{array}\right]$

$\mathrm{pv}≔\mathrm{PositionVector}\left(\left[3\,4\right]\right)\:$

$\mathrm{About}\left(\mathrm{pv}\right)$

$\left[\begin{array}{cc}\mathrm{Type:}& \mathrm{Position\; Vector}\\ \mathrm{Components:}& \left[3\,4\right]\\ \mathrm{Coordinates:}& {\mathrm{cartesian}}_{x,y}\\ \mathrm{Root\; Point:}& \left[0\,0\right]\end{array}\right]$

$\mathrm{rv2}≔\mathrm{evalVF}\left(\mathrm{vf}\,⟨3\,4⟩\right)\:$

$\mathrm{About}\left(\mathrm{rv2}\right)$

$\left[\begin{array}{cc}\mathrm{Type:}& \mathrm{Rooted\; Vector}\\ \mathrm{Components:}& \left[4\,12\right]\\ \mathrm{Coordinates:}& {\mathrm{cartesian}}_{x,y}\\ \mathrm{Root\; Point:}& \left[3\,4\right]\end{array}\right]$