MITACS Seminar Series on Mathematics of Computer Algebra and Analysis

Subresultants in Roots.

Professor Hoon Hong, North Carolina State University

11:00am, Friday April 18th, 2008, in K9509.

Slides from Talk


Subresultants, the generalization of resultants, play fundamental role in
computational algebra and algebraic geometry.

Subresultants are defined in terms of the coefficients of the polynomials, which
is convenient for computation (algebra), but not so useful for reasoning (geometry).

In this talk, we review  various "nice" expressions for subresultants  which are
useful  for  reasoning. In  particular,  we show  several  ways to  express the
subresultants in terms of the roots of the polynomials.

We hope that these expressions  will be found useful in  discovering interesting
geometric properties, such as geometric basis for gap structure, root separation
bound for non-square-free polynomials, etc.