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VectorCalculus

 evalVF
 evaluate a vector field at a point

 Calling Sequence evalVF(F, v)

Parameters

 F - vector field or a Vector valued procedure; specify the components of the vector field v - free or position Vector; specify the point at which to evaluate the vector field

Description

 • The command evalVF(F, v) evaluates the vector field F at the point v.  The result is a rooted Vector with root point v.
 • The parameters, F and v, must have the same dimension, but do not need to be defined in the same coordinate system.
 • The vector field parameter, F, can also be specified as a Vector-valued procedure, in which case this procedure is evaluated at the coordinates of the Vector v.

Examples

 > $\mathrm{with}\left(\mathrm{VectorCalculus}\right):$
 > $\mathrm{ev}≔\mathrm{evalVF}\left(\left(x,y,z\right)→\mathrm{RootedVector}\left(\mathrm{root}=\left[1,0,1\right],\left[\mathrm{cos}\left(x\right),\mathrm{sin}\left(y\right),z\right]\right),\mathrm{PositionVector}\left(\left[\mathrm{π},\frac{\mathrm{π}}{2},0\right]\right)\right)$
 ${\mathrm{ev}}{≔}\left[\begin{array}{r}{-}{1}\\ {1}\\ {0}\end{array}\right]$ (1)
 > $\mathrm{About}\left(\mathrm{ev}\right)$
 $\left[\begin{array}{cc}{\mathrm{Type:}}& {\mathrm{Rooted Vector}}\\ {\mathrm{Components:}}& \left[{-}{1}{,}{1}{,}{0}\right]\\ {\mathrm{Coordinates:}}& {{\mathrm{cartesian}}}_{{x}{,}{y}{,}{z}}\\ {\mathrm{Root Point:}}& \left[{\mathrm{π}}{,}\frac{{1}}{{2}}{}{\mathrm{π}}{,}{0}\right]\end{array}\right]$ (2)
 > $\mathrm{SetCoordinates}\left({\mathrm{polar}}_{r,\mathrm{θ}}\right)$
 ${{\mathrm{polar}}}_{{r}{,}{\mathrm{θ}}}$ (3)
 > $F≔\mathrm{VectorField}\left(⟨{r}^{2}\mathrm{θ},-\mathrm{θ}⟩\right)$
 ${F}{≔}\left({{r}}^{{2}}{}{\mathrm{θ}}\right){\stackrel{{_}}{{e}}}_{{r}}{-}{\mathrm{θ}}{\stackrel{{_}}{{e}}}_{{\mathrm{θ}}}$ (4)
 > $\mathrm{simplify}\left(\mathrm{evalVF}\left(F,⟨1,\frac{\mathrm{π}}{2}⟩\right)\right)$
 $\left[\begin{array}{c}\frac{{1}}{{2}}{}{\mathrm{π}}\\ {-}\frac{{1}}{{2}}{}{\mathrm{π}}\end{array}\right]$ (5)
 > $\mathrm{evalVF}\left(\left(a,b\right)→⟨{a}^{2},{b}^{2}⟩,\mathrm{Vector}\left(\left[0,1\right],\mathrm{attributes}=\left[\mathrm{coordinates}=\mathrm{cartesian}\right]\right)\right)$
 $\left[\begin{array}{c}{1}\\ \frac{{1}}{{4}}{}{{\mathrm{π}}}^{{2}}\end{array}\right]$ (6)