Mathemagix

[Adrien Poteaux <address@concealed>]

Maybe the word is not good. They are also called branch points or 
discriminant points. The roots of the discriminant in the second 
variable, points above which you have Puiseux series and not classical 
power series.

So I mean an analytic continuation process : you start from the base 
point, compute power series that you evaluate at an other point, where 
you compute power series, and so on along the path you want to follow. 
Here the radius convergence of power series is at least the distance to 
the nearest critical point. So, to my knowledge, you need to have bound 
on the distance to the nearest critical point to follow the analytic 
continuation process (at least if you want some certification).

Oh, and I am just seeing that I did not precised that we consider 
bivariate polynomials. The misunderstanding may come from this point, sorry.

Adrien

Joris van der Hoeven wrote:

> On Fri, Jan 23, 2009 at 03:39:09PM +0100, Adrien Poteaux wrote:
>  
>
> > In my current work with Andre Galligo, I need some analytic continuation 
> > process for high degree polynomials (something like 100), and I am 
> > looking to make this using mathemagix (because it includes fast 
> > algorithms which are needed with such degrees, and also because there is 
> > some time that I want to use this).
> >
> > In some talks given by Joris, he showed some example where mathemagix 
> > was making some analytic continuation process. On the mathemagix 
> > website, I saw that this was include in the analyziz package, but nor 
> > more information are given here. As I am not used to this language for 
> > the moment, I would like to know which functions could be usefull for my 
> > purpose, what is really done in mathemagix, and what is not.
> >
> > More details about what we need : we would like to make analytic 
> > continuation along some paths (3 in practice) without of course 
> > computing all the singular / critical points (which are too many with 
> > such degree). Thus, the two points I see are the analytic continuation 
> > process on one hand, and the detection of close singularities during the 
> > process on the other hand.
> >
> > These subjects have been studied in Joris paper's, where he says that he 
> > started the implementation in mathemagix, but is this work ended and 
> > available ? And if yes, what do we have to use ?
> >    
>
> I do not really understand what you mean by analytic continuation of 
> polynomials.
> Since polynomials have no singularities, you just want to compute Taylor 
> shifts?
>
> Best wishes, Joris
>