Difficulties in the Computation of the Kretschmann scalar

[Hamilton]

Hello,
Thanks to all of you for the help that you provide so that we can move forward.

I need help about the computation of the Kretschmann scalar without using software, I face to some difficulties on its computation for instance in the case of Schwarzschild metric. Could some one help me with some reference containing the steps of this computation, and how use properties of symmetries of the Riemann tensor to avoid the computation of all its 256 components but only the non zeros components.
Thank you

 

[robphy]

This might help
http://physicspages.com/2014/04/06/riemann-tensor-counting-independent-components/