The call GetSpace(v) returns a module which encodes the vector space to which the rooted Vector v belongs.  For details about the representation of vector spaces in the VectorCalculus package, see VectorSpace.

For details about the different Vectors of the VectorCalculus package, see VectorCalculus,Details.

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

$f≔\mathrm{Vector}\left(\left[1\,t\right]\,\mathrm{coords}=\mathrm{polar}\left[r,\mathrm{\theta }\right]\right)$

$v≔\mathrm{simplify}\left(\mathrm{TangentVector}\left(f\right)\right)$

$v≔\left[\begin{array}{c}0\\ 1\end{array}\right]$

$\mathrm{vs}≔\mathrm{GetSpace}\left(v\right)$

$\mathrm{vs}≔\mathbf{module}\left(\right)\mathbf{local}\mathrm{\_origin}\,\mathrm{\_coords}\,\mathrm{\_coords\_dim}\;\mathbf{export}\mathrm{GetCoordinates}\,\mathrm{GetRootPoint}\,\mathrm{Vector}\,\mathrm{eval}\;\mathbf{end\; module}$

$\mathrm{vs}:-\mathrm{GetCoordinates}\left(\right)$

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

$\mathrm{vs}:-\mathrm{GetRootPoint}\left(\right)$