Differential Forms


Run the following code to initialize $\LaTeX$ output and load some macros, either by clicking on "Evaluate" or by typing Shift+Enter.

Now enter a line element in the box below, adapting the given code as needed. First declare any parameters or functions, then provide a list of (orthogonal) coordinates using the MakeC command as shown below (note the double parentheses). Finally, use the Makeg command to enter both the signature (number of $-$ signs) and the diagonal coefficients ($g_{ii}$) of the line element $ds^2=g_{ij}dx^idx^j$. The result should be the volume element $\omega$.


Now run the Sage code in the boxes below. (You can also enter your own code.)