Mathematics – Algebraic Geometry
Scientific paper
2008-01-20
Mathematics
Algebraic Geometry
16 pages, minor changes made, references added
Scientific paper
Consider an ideal $I \subset R = \bC[x_1,...,x_n]$ defining a complex affine variety $X \subset \bC^n$. We describe the components associated to $I$ by means of {\em numerical primary decomposition} (NPD). The method is based on the construction of {\em deflation ideal} $I^{(d)}$ that defines the {\em deflated variety} $\dXd$ in a complex space of higher dimension. For every embedded component there exists $d$ and an isolated component $\dYd$ of $\dId$ projecting onto $Y$. In turn, $\dYd$ can be discovered by existing methods for prime decomposition, in particular, the {\em numerical irreducible decomposition}, applied to $\dXd$. The concept of NPD gives a full description of the scheme $\Spec(R/I)$ by representing each component with a {\em witness set}. We propose an algorithm to produce a collection of witness sets that contains a NPD and that can be used to solve the {\em ideal membership problem} for $I$.
Leykin Anton
No associations
LandOfFree
Numerical primary decomposition does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Numerical primary decomposition, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Numerical primary decomposition will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-593294