The call GetSpace(v) returns a module which encodes the vector space to which the rooted Vector v belongs.

The Student[VectorCalculus] package uses the same Vector data structures as the VectorCalculus package. For details about the various types of Vectors in these packages, see VectorCalculus,Details.

For details about the representation of vector spaces, see Student[VectorCalculus][VectorSpace].

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

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

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

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

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

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

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

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

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