General Relativity in Maxima and Mathematica
Maxima script for the Ricci tensor of a spherically symmetric metric (in the coordinates r,t) [wxm, pdf, TeX]
Maxima script for the Ricci tensor of a spherically symmetric metric in the static case (coordinate r) [wxm, pdf, tex]
V.T.Toth Maxima script for the derivation of Schwarzschild metric [wxm, pdf, TeX]
The plot produced by this script should look like in the pdf file, i.e. like the [ png figure for the TeX file ]
However, in modern implementations of Maxima some options of plot3d (and hence wxplot3d in wxmaxima) like 'legend' do not work.
In this case use [ another wxm script ] also showing many plots from a Maxima tutorial.
Detailed explanations to the Toth's script are given by Anastasiya M.Schitova from Yaroslavl State University [ pdf , TeX ]
Anastasiya has also written a script with derivation of Schwarzschild and Reissner–Nordström metric, which is described in the above reference. Here is the separate script: [wxm, pdf, TeX]