By default, free Vectors, rooted Vectors and vector fields created by commands in the Student[VectorCalculus] package are displayed using basis format, that is, as a sum of scalar multiples of basis vectors.  Basis vectors are displayed by using the letter "e" subscripted by a coordinate name. If the Vector displayed is a vector field, the basis vectors display with an overbar.

The BasisFormat(fmt) calling sequence determines whether basis format style is used.  If fmt is true, free Vectors, rooted Vectors and vector fields are displayed using basis format.  If fmt is false, free Vectors, rooted Vectors and vector fields are displayed using standard Vector notation.

The position Vectors, being Vectors that are always in cartesian coordinates rooted at the origin, are always displayed in standard Vector notation. The BasisFormat(fmt) calling sequence has no effect on the position Vector.

Note: In standard Vector notation, there is no visual distinction between vector fields and the other Vectors.

The BasisFormat command returns the basis format setting when the command was invoked, not the new setting.

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

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

$\mathrm{true}$

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

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

$\mathrm{fv}≔⟨2\,3⟩$

$\mathrm{rv}≔\mathrm{RootedVector}\left(\mathrm{root}=\left[1\,\mathrm{\pi }\right]\,\left[2\,\frac{\mathrm{\pi }}{2}\right]\right)$

$\mathrm{rv}≔\left[\begin{array}{c}2\\ \frac{\mathrm{\pi }}{2}\end{array}\right]$

$\mathrm{vf}≔\mathrm{VectorField}\left(⟨r^2\,\frac{1}{\mathrm{\theta }}⟩\right)$

$\mathrm{pv}≔\mathrm{PositionVector}\left(\left[1\,\mathrm{\theta }\right]\right)$

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

$\mathrm{BasisFormat}\left(\mathrm{false}\right)$

$\mathrm{true}$

$\mathrm{fv}$

$\mathrm{rv}$

$\left[\begin{array}{c}2\\ \frac{\mathrm{\pi }}{2}\end{array}\right]$

$\mathrm{vf}$

$\left[\begin{array}{c}{r}^2\\ \frac{1}{\mathrm{\theta }}\end{array}\right]$

$\mathrm{pv}$

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