On Thursday, January 5, 2017 at 3:27:46 PM UTC, Eric Gourgoulhon wrote:
>
> Le jeudi 5 janvier 2017 10:35:27 UTC+1, Dima Pasechnik a écrit :
>>
>>
>> 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.
>>
>>
> Yes indeed, but then what about dealing with a second volume element
> sqrt(-z') (arising from another metric): we cannot work both in the
> polynomial polynomial ring modulo the ideal generated by w^2+z and that
> modulo the ideal generated by w'^2 + z', can we?
>
we can work modulo the ideal generated by w^2+z and w'^2+z', sure, why not?
>
> However, let me take the opportunity of this discussion to mention that
> all the manifold stuff, as implemented in src/sage/manifolds, depends very
> weakly on the Symbolic Ring: all the coordinate calculus is encapsulated in
> the abstract base class CoordFunction
> <http://doc.sagemath.org/html/en/reference/manifolds/sage/manifolds/coord_func.html#sage.manifolds.coord_func.CoordFunction>,
>
> which, at the moment, has a single concrete derived class:
> CoordFunctionSymb
> <http://doc.sagemath.org/html/en/reference/manifolds/sage/manifolds/coord_func_symb.html#sage.manifolds.coord_func_symb.CoordFunctionSymb>.
>
> Only the latter involves the Symbolic Ring. In the future, we may conceive
> other concrete derived classes, based on fraction fields of polynomial
> rings, as Samuel and you suggest, or sympy, or Giac, or even numerical
> methods.
>
> Best wishes,
>
> Eric.
>
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