On Wednesday, January 4, 2017 at 8:24:22 PM UTC, Eric Gourgoulhon wrote:
>
> Hi Samuel,
>
> Le mercredi 4 janvier 2017 20:49:54 UTC+1, Samuel Lelievre a écrit :
>>
>>
>>
>> It's of course a good thing to track the issue, but on the other side,
>> why work in the Symbolic Ring?
>>
>>
> It's because I need to consider sqrt(-z), so that I cannot stay with 
> rational functions. 
>

I woud have picked one more variable, w, and set w^2=-z.
Now everything is polynomial again...

 

> Actually sqrt(-z) is the volume element of the Tomimatsu-Sato 3-metric:
>
> http://nbviewer.jupyter.org/github/sagemanifolds/SageManifolds/blob/master/Worksheets/v1.0/SM_Tomimatsu-Sato_3p1.ipynb
> Note that, despite this issue with the volume element, Sage is doing 
> pretty well with this complicated metric (see e.g. the huge expression of 
> the Ricci scalar in Out[24]): all Einstein equations are passed.
>
> Best regards,
>
> Eric.
>

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