Run the following code to initialize $\LaTeX$ output and load (frontend to) the differential forms package, 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
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 coefficients $h^i$ of an
orthonormal basis $\sigma^i=h^i\,dx^i$ (no sum) of 1-forms in orthogonal
coordinates. The result should be the line element in tensor notation.
Use the command MakeGam() to compute and display the connection
1-forms $\omega^i{}_j=\Gamma^i{}_{jk}\sigma^k$ for an orthonormal basis.
(You can then list the nonzero connection coefficients $\Gamma^i{}_{jk}$
with the command nab.display().)
Use the command MakeOm() to compute and display the curvature
2-forms $\Omega^i{}_j=\frac12R^i{}_{jkl}\sigma^k\wedge\sigma^l$ for an
orthonormal basis. (You can then print specific curvature components
$R^i{}_{jkl}$ with the command riem[i,j,k,l]).
Use the command below to express the curvature 2-forms in terms of an orthonormal basis (here written as $e^i$ rather than $\sigma^i$).