MITACS Seminar Series on Mathematics of Computer Algebra and Analysis

Regular Chains: Theory and Practice

Paul Vrbik, Department of Computer Science, University of Western Ontario

Talk Slides

Wednesday February 23rd, 2011, at 3:30pm, in K9509.

Abstract: 

Regular chains are one of the only real alternatives to Groebner bases (GB) 
for solving systems of polynomials.  Using regular chains instead of GB is becoming
more common; evidenced by regular chains supplanting Groebner bases in
Maple's "solve" command for difficult input polynomial systems. Why?

I start with the basic notions of primary decomposition, saturation ideals,
and triangular sets. Then refine these ideas to discuss the fundamental
theoretical properties of regular chains and how one uses them to
decompose polynomial systems.

Once a sufficient theoretical groundwork is laid I will demonstrate how the 
recursive definitions lend themselves naturally to algorithms and show that
these algorithms produce output preferable to that of a GB.