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.
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.