Thanks for your reply, David. I didn't know Singular could factor
over the ring of formal power series. I'll check it out.
Alex
On Jan 23, 11:09 pm, daveloeffler <dave.loeff...@gmail.com> wrote:
> 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 <tortoise.s...@gmail.com> 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
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