Hi Daniel,
I'm gald that my package can help you!
As for your question, in this package, you can write the expresssion explicitly to calculate as following:
Here I use Schwarzschild metric as an example. The function STCalcComponents is the latest version of the function STSpecify in the post above. Please download the latest package in the GitHub: SpTm if you need.
There is another package I wrote for better tensor computations - STensor | Wolfram Language Paclet Repository. It provides more convenient interface for you to compute tensor expression. In this paclet, we can caclulate the same Kretschmann scalar as following:
Personally, I prefer the second package - where tensor becomes something as integer and complex number in Mathematica. We can set its value to symbol and do computation. There is a guide documentation for each function just as built-in function. PacletInstall and Needs will handle everything and we do not need to worry about placing the files correctly.
These two packages are not complete. I will add more functions in it in the future. The Kretschmann scalar will be on the list. Thank you for your helpful advice! :)
