On Thursday, January 5, 2017 at 9:16:45 AM UTC, Eric Gourgoulhon wrote:
>
>
>
> Le mercredi 4 janvier 2017 23:41:00 UTC+1, Dima Pasechnik a écrit :
>>
>>
>>
>> On Wednesday, January 4, 2017 at 9:06:44 PM UTC, Eric Gourgoulhon wrote:
>>>
>>> Le mercredi 4 janvier 2017 21:47:00 UTC+1, Dima Pasechnik a écrit :
>>>>
>>>>
>>>>
>>>> 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...
>>>>
>>>>
>>> But z is not a variable: it is (minus) the determinant of the
>>> Tomimatsu-Sato metric w.r.t. to the coordinates (x,y,phi), which turns out
>>> to be a rational function in (x,y). For further computations, the explicit
>>> expression of the volume element sqrt(-z) in terms of (x,y) is required.
>>>
>> So I don't see how I could use something like w^2=-z with w being a
>>> function of (x,y) without taking a square root.
>>>
>>
>> and, indeed, it will be there, as w=sqrt(-z), no? That is, in effect
>> you'd be computing in the polynomial ring modulo the ideal
>> generated by w^2+z.
>>
>>
> Thanks for your suggestion; however, I am not sure if this could fully
> work: some computations require to take derivatives, i.e. to evaluate
> d/dx (sqrt(-z)), where z is the rational function of (x,y) discussed
> above. Could this work in our framework?
>
d/dx (-z)^{1/2}=-1/(2(-z)^{1/2})dz/dx=-(dz/dx)/(2w), and so you can carry
one staying within rational functions in your variables original variables
and w.
It's of course hard to say how far this will get you without looking at the
details of your computation (e.f. perhaps you might need
to integrate at some point?), but
hopefully, to the point where you need to do numerical evaluations anyway...
> Best regards,
>
> Eric.
>
--
You received this message because you are subscribed to the Google Groups
"sage-devel" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to sage-devel+unsubscr...@googlegroups.com.
To post to this group, send email to sage-devel@googlegroups.com.
Visit this group at https://groups.google.com/group/sage-devel.
For more options, visit https://groups.google.com/d/optout.
