Curvature of the Sphere

Initialization

Run the following code to initialize $\LaTeX$ output and set up the sphere, either by clicking on "Evaluate" or by typing Shift+Enter.
(This is raw Sage code, with no macros.)
(The result should be the volume element $\omega$. Edit as desired.)

Code

Now run the Sage code in the boxes below to determine the connection 1-form, curvature 2-form, and Gauss curvature.
(You can also enter your own code.)