Important: The linalg package has been deprecated. Use the superseding command VectorCalculus[VectorPotential], instead.

- For information on migrating linalg code to the new packages, see examples/LinearAlgebraMigration.

The function vecpotent determines whether a given vector function has a vector potential, and determines that vector potential if it exists.

The function returns true if the function f has a vector potential, and false if it does not.  The vector potential exists if and only if the divergence of f is zero.

If a vector potential for f exists, it will be assigned to the name given in the third argument V.  If vecpotent returns true, then V will be assigned a vector function such that curl V = f.

The command with(linalg,vecpotent) allows the use of the abbreviated form of this command.

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

$f≔\left[x^{2}y\,-\frac{1}{2}x{y}^2\,-xyz\right]$

$f≔\left[x^{2}y\,-\frac{x{y}^2}{2}\,-xyz\right]$

$\mathrm{vecpotent}\left(f\,\left[x\,y\,z\right]\,'V'\right)$

$\mathrm{true}$

$\mathrm{print}\left(V\right)$

$\left[\begin{array}{ccc}-\frac{x{y}^{2}z}{2}& -x^{2}yz& 0\end{array}\right]$

$g≔\left[x^2\,y^2\,z^2\right]$

$g≔\left[x^2\,y^2\,z^2\right]$

$\mathrm{vecpotent}\left(g\,\left[x\,y\,z\right]\,'G'\right)$

$\mathrm{false}$