The GetCoordinates(v) calling sequence returns the coordinate system attribute of the Vector v.  If v is not specified, the default coordinate system is returned.

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

$\mathrm{GetCoordinates}\left(\right)$

$\mathrm{cartesian}$

$\mathrm{v1}≔\mathrm{Vector}\left(⟨\sin \left(t\right)\,\cos \left(t\right)\,t^2⟩\right)$

$\mathrm{GetCoordinates}\left(\mathrm{v1}\right)$

$\mathrm{cartesian}$

$\mathrm{v2}≔\mathrm{VectorField}\left(⟨r\,0\,0⟩\right)$

$\mathrm{GetCoordinates}\left(\mathrm{v2}\right)$

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

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

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

$\mathrm{GetCoordinates}\left(⟨a\,b⟩\right)$

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

$\mathrm{GetCoordinates}\left(\mathrm{v1}\right)$

$\mathrm{cartesian}$