On Saturday, October 17, 2015 at 8:49:28 PM UTC+2, Francesco Bonazzi wrote:
>
>
>
> On Saturday, 17 October 2015 17:52:38 UTC+2, Imran Ali wrote:
>
>>
>> But this result does not correspond to the hand calculations of Thomas 
>> Moore :
>>
>>
> Do you know that unlike matrices tensors don't have defined components? I 
> mean, you may vary their valence (i.e. raise and lower the indices), and 
> you'll get different components.
>
> I did not verify it by hand, but I guess that if you raise the first index 
> of Thomas Moore's Riemann tensor, you'll get the output by SymPy.
>

Ah of course! He has calculated the covariant form of the 
Riemann-Christoffel tensor. 

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