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VectorCalculus

 GetSpace
 return the VectorSpace of a rooted Vector

 Calling Sequence GetSpace(v)

Parameters

 v - Vector; a rooted Vector

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{VectorCalculus}\right):$
 > $f≔\mathrm{Vector}\left(\left[1,t\right],\mathrm{coords}={\mathrm{polar}}_{r,\mathrm{θ}}\right)$
 ${f}{:=}{{e}}_{{r}}{+}\left({t}\right){{e}}_{{\mathrm{θ}}}$ (1)
 > $v≔\mathrm{simplify}\left(\mathrm{TangentVector}\left(f\right)\right)$
 ${v}{:=}\left[\begin{array}{r}{0}\\ {1}\end{array}\right]$ (2)
 > $\mathrm{vs}≔\mathrm{GetSpace}\left(v\right)$
 ${\mathrm{vs}}{:=}{\mathbf{module}}\left({}\right)\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathbf{local}}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathrm{_origin}}{,}{\mathrm{_coords}}{,}{\mathrm{_coords_dim}}{;}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathbf{export}}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathrm{GetCoordinates}}{,}{\mathrm{GetRootPoint}}{,}{\mathrm{Vector}}{;}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathbf{end module}}$ (3)
 > $\mathrm{vs}:-\mathrm{GetCoordinates}\left(\right)$
 ${{\mathrm{polar}}}_{{r}{,}{\mathrm{θ}}}$ (4)
 > $\mathrm{vs}:-\mathrm{GetRootPoint}\left(\right)$
 $\left(\sqrt{{{\mathrm{cos}}{}\left({t}\right)}^{{2}}{+}{{\mathrm{sin}}{}\left({t}\right)}^{{2}}}\right){{e}}_{{r}}{+}\left({\mathrm{arctan}}{}\left({\mathrm{sin}}{}\left({t}\right){,}{\mathrm{cos}}{}\left({t}\right)\right)\right){{e}}_{{\mathrm{θ}}}$ (5)