Hmm. I'm not a geometer myself, but nobody else seems to have bitten
on this one...
If CC[[x_1, ..., x_n]] is the local ring of CC^n at the origin, we can
try to factorise the defining ideal I of V in this ring. This isn't
the same as your ring CC{x_1, ..., x_n} of germs of holomorphic
functions, but it's probably close enough, and gives the same answer
in your example.
Sage at present doesn't natively support multivariate power series
rings, but Sage includes Singular, which does support these rings, and
can work with their ideals and Groebner bases. You can get a Singular
command line from the Sage console by typing "singular.console()". I
suggest you look at the Singular documentation.
David
On Jan 22, 12:46 am, Alex Raichev <[email protected]> wrote:
> Hi all:
>
> I have a geometry question. Given an ALGEBRAIC variety V in CC^n
> defined by a single polynomial and given a point p in V, how do you
> compute the number of (distinct) irreducible ANALYTIC components of V
> passing through p?
>
> For example, let f = y^2 -x^2*(1 +x). Then the variety V(f) has two
> irreducible analytic components passing through (0,0), one for each
> factor of the decomposition
>
> f = (y -x*sqrt(1+x)) *(y +x*sqrt(1+x))
>
> in CC{x,y}, the ring of power series convergent in a neighborhood of
> (0,0).
>
> Alex
--~--~---------~--~----~------------~-------~--~----~
To post to this group, send email to [email protected]
To unsubscribe from this group, send email to
[email protected]
For more options, visit this group at
http://groups.google.com/group/sage-support
URLs: http://www.sagemath.org
-~----------~----~----~----~------~----~------~--~---
