MITACS Seminar Series on Mathematics of Computer Algebra and Analysis
Subresultants in Roots.
Professor Hoon Hong, North Carolina State University
Abstract: 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.