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

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

curl(f, v) computes the curl of f with respect to v, where f is a three-dimensional function of the three variables v.  When the third argument is not given, the curl of f is computed in the Cartesian coordinate system.

If the optional third argument co is of the form coords = coords_name or coords = coords_name([const]), curl will operate on commonly used orthogonally curvilinear coordinate systems. See ?coords for the list of the coordinate systems supported by Maple.

If co is a list of three elements which specify the scale factors, curl will operate on orthogonally curvilinear coordinate systems.

To compute the curl in other orthogonally curvilinear coordinate systems, use the addcoords routine.

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

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

$f≔\left[x^2\,xz\,y^{2}z\right]\:$$v≔\left[x\,y\,z\right]\:$

$\mathrm{curl}\left(f\,v\right)$

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

$g≔\left[r\,\sin \left(\mathrm{\theta }\right)\,z\right]\:$$v≔\left[r\,\mathrm{\theta }\,z\right]\:$

$\mathrm{curl}\left(g\,v\,\mathrm{coords}=\mathrm{cylindrical}\right)$

$\left[\begin{array}{ccc}0& 0& \frac{\sin \left(\mathrm{\theta }\right)}{r}\end{array}\right]$

$h≔\left[1\,r\,1\right]\:$

$\mathrm{curl}\left(g\,v\,h\right)$

$\left[\begin{array}{ccc}0& 0& \frac{\sin \left(\mathrm{\theta }\right)}{r}\end{array}\right]$

$i≔\left[r\,\sin \left(\mathrm{\theta }\right)r\,\cos \left(\mathrm{\phi }\right)r\right]\:$$v≔\left[r\,\mathrm{\theta }\,\mathrm{\phi }\right]\:$

$\mathrm{curl}\left(i\,v\,\mathrm{coords}=\mathrm{spherical}\right)$

$\left[\begin{array}{ccc}\frac{\cos \left(\mathrm{\theta }\right)\cos \left(\mathrm{\phi }\right)}{\sin \left(\mathrm{\theta }\right)}& -2\cos \left(\mathrm{\phi }\right)& 2\sin \left(\mathrm{\theta }\right)\end{array}\right]$