The ConvertVector command converts Cartesian free Vectors, rooted Vectors and position Vectors among themselves by specifying the desired type. If v is not a Cartesian Vector an error is raised.

If form is rooted, the root point can be specified as a list or a free Vector with the extra optional parameter root. If root is a list, it is interpreted in Cartesian coordinates, if it is a free Vector in non-Cartesian coordinates, an appropriate transformation is made to obtain a Cartesian root.

If form is rooted, v is a free, rooted or position Vector and root is provided, the result is the Vector rooted at root.

If form is rooted, v is a position Vector and root is not provided, then the Vector is rooted at the Cartesian origin.

If form is rooted, v is a free Vector and root is not provided an error is raised.

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

$\mathrm{ConvertVector}\left(\mathrm{PositionVector}\left(\left[1\,p\right]\,\mathrm{parabolic}\right)\,'\mathrm{rooted}'\right)$

$\left[\begin{array}{c}\frac{1}{2}-\frac{p^2}{2}\\ p\end{array}\right]$

$\mathrm{pv}≔\mathrm{PositionVector}\left(\left[p\cos \left(p\right)\,p\sin \left(p\right)\right]\,\mathrm{cartesian}\left[x,y\right]\right)$

$\mathrm{pv}≔\left[\begin{array}{c}p\cos \left(p\right)\\ p\sin \left(p\right)\end{array}\right]$

$\mathrm{v1}≔\mathrm{ConvertVector}\left(\mathrm{pv}\,'\mathrm{free}'\right)$

$\mathrm{v2}≔\mathrm{ConvertVector}\left(\mathrm{pv}\,'\mathrm{rooted}'\right)$

$\mathrm{v2}≔\left[\begin{array}{c}p\cos \left(p\right)\\ p\sin \left(p\right)\end{array}\right]$

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

$\left[\begin{array}{cc}\mathrm{Type:}& \mathrm{Rooted\; Vector}\\ \mathrm{Components:}& \left[p\cos \left(p\right)\,p\sin \left(p\right)\right]\\ \mathrm{Coordinates:}& {\mathrm{cartesian}}_{x,y}\\ \mathrm{Root\; Point:}& \left[0\,0\right]\end{array}\right]$

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

$\mathrm{v3}≔\mathrm{ConvertVector}\left(\mathrm{pv}\,'\mathrm{rooted}'\,\left[1\,1\right]\right)$

$\mathrm{v3}≔\left[\begin{array}{c}p\cos \left(p\right)\\ p\sin \left(p\right)\end{array}\right]$

$\mathrm{GetRootPoint}\left(\mathrm{v3}\right)$

$\mathrm{v4}≔\mathrm{ConvertVector}\left(\mathrm{pv}\,'\mathrm{rooted}'\,\mathrm{Vector}\left(⟨1\,\frac{\mathrm{\pi }}{2}⟩\,\mathrm{coords}=\mathrm{polar}\left[u,v\right]\right)\right)$

$\mathrm{v4}≔\left[\begin{array}{c}p\cos \left(p\right)\\ p\sin \left(p\right)\end{array}\right]$

$\mathrm{GetRootPoint}\left(\mathrm{v4}\right)$