Symbolic Computation Group

David R. Cheriton School of Computer Science
University of Waterloo, Waterloo, Ontario, Canada

The intersection of subfields of K(x)
Michael Zieve, Institute for Advanced Study, Princton, USA
Friday, Oct 10, 2008, at U. of Waterloo.

Abstract:

I will discuss this problem: given rational functions f and g over a field K , determine whether there are nonconstant rational functions u and v over K such that u(f(x)) = v(g(x)) . An equivalent problem is to compute the intersection of two fields which lie between K and K(x) . This has been solved completely in case f and g are polynomials and K has characteristic zero, but it remains open in nearly all other cases. I will present new and old results, examples, and algorithms for this problem.

 

Last modified on Sunday, 04 November 2012, at 20:42 hours.