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! :)

Thanks for your attention, sir!

I'm still a learner about both General Relativity and Mathematica. I'm going to learn more knowledge and make my package perfect.

And I'm learning to using more Wolfram techniques. I'm going to try Wolfram Paclet Repository to host my package.

Best Regards.