MITACS Seminar Series on Mathematics of Computer Algebra and Analysis

Primary decomposition and numerical homotopy continuation.

Professor Anton Leykin

Department of Mathematics, Statistics, and Computer Science, University of Illinois.

9:30am, Monday October 6th, 2008, in K9509.

Abstract: 

We propose a new method for computing associated primes of a polynomial
ideal I. Our symbolic approach proceeds by constructing the ideal I^(d),
a deflation of I in a larger polynomial ring, with the property that each
associated prime of I is a projection of an associated minimal prime of I^(d).

Another exciting side of this method is the possibility of employing the 
numerical irreducible decomposition: a brief introduction to numerical
homotopy continuation methods will be provided. This gives rise to the
concept of numerical primary decomposition, which could provide a
numerical alternative to Groebner bases: e.g., the ideal membership problem
can be solved numerically.