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 potential determines whether a given vector function is derivable from a scalar potential, and determines that potential if it exists.

The function returns true if the function f has a scalar potential, and false if it does not.

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

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

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

$f≔\left[2xy+y^3\,x^2+3x{y}^2\right]$

$f≔\left[y^3+2xy\,3x{y}^2+x^2\right]$

$\mathrm{potential}\left(f\,\left[x\,y\right]\,'F'\right)$

$\mathrm{true}$

$F$

$y\left(x{y}^2+x^2\right)$

$g≔\left[2x\,2y\,2z\right]$

$g≔\left[2x\,2y\,2z\right]$

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

$\mathrm{true}$

$G$

$x^2+y^2+z^2$