Run the following code to initialize $\LaTeX$ output and load (Tevian's frontend to) the differential forms package, either by clicking on "Evaluate" or by typing Shift+Enter.
Uncomment one of the following code blocks to select the appropriate
orthogonal coordinate system.
The output should be the volume element $\omega$.
(The default is spherical coordinates.)
Now run the Sage code in the boxes below. (You can also enter your own code.)
Notation:
The 1-form $\alpha$ is defined in an orthonormal basis, but the gradient and
curl are given in a coordinate basis.
You can add the missing factors by hand.