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    $\begingroup$ Please be more specific. What exactly do you want to do? $\endgroup$ Commented Mar 6, 2012 at 10:32
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    $\begingroup$ I've heard that this book is pretty good, and the authors developed some Mathematica framework for differential geometry which comes with the book. Did not have a chance to get my hands on it though. $\endgroup$ Commented Mar 6, 2012 at 10:33
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    $\begingroup$ @user450 In the future, it is useful if you include information as to what you have already looked at (such as the Ricci package) or considered, and what you found missing. $\endgroup$ Commented Mar 6, 2012 at 15:07
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    $\begingroup$ I recommend xAct package for tensor calculus (not only for this) xact.es, there are big chances that is similar to the future Mathematica built-in functionality. $\endgroup$ Commented Mar 7, 2012 at 3:06
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    $\begingroup$ http://en.wikipedia.org/wiki/Tensor_software $\endgroup$ Commented Mar 12, 2012 at 14:43