Top Free Mathematica Packages for Calculating GR Tensors and Derivatives

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Hi,

I am interested in obtaining a FREE mathematica package that can:

1) Calculate standard GR tensors (connections, Ricci, Einstein etc.)
2) take covariant derivatives
3) and define tensors

Does anyone know of a good Mathematica package?
 
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For Maxima (which is free), there is a package called ctensor. Dunno about Mathematica, since I consider my time on Earth too valuable to waste it on proprietary programming languages.
 
There is a package for Mathematica called Ricci, which is free, just the package not Mathematica. You can search for it on the web and download it.
 
There is also GTensor2 for maple which runs quite well under MATLAB with the symbolic toolbox.
 
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