#### Presentation Title

Determing the Topologies of Real Zero Sets of Polynomials with Two Variables and Five Terms

#### Faculty Mentor

Maurice Rojas

#### Start Date

18-11-2017 10:00 AM

#### End Date

18-11-2017 11:00 AM

#### Location

BSC-Ursa Minor 109

#### Session

Poster 1

#### Type of Presentation

Poster

#### Subject Area

physical_mathematical_sciences

#### Abstract

A fundamental problem in many applications is determining the topology of the set of real zeros of a polynomial. The A-discriminant is a central tool derived by Gelfand, Kapranov and Zelevinsky that tells us when a polynomial has degenerate roots. Degenerate roots, in turn, determine when the topology of a zero set changes. We explore these topics by creating a MATLAB program that draws A-discriminant curves for polynomials in two variables with five terms. The program finds all discriminant chambers and automatically computes the topology of the zero set of any bivariate pentanomials. This automatic topology computation for high degree polynomials will be quite useful for the real algebraic geometry community.

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Determing the Topologies of Real Zero Sets of Polynomials with Two Variables and Five Terms

BSC-Ursa Minor 109

A fundamental problem in many applications is determining the topology of the set of real zeros of a polynomial. The A-discriminant is a central tool derived by Gelfand, Kapranov and Zelevinsky that tells us when a polynomial has degenerate roots. Degenerate roots, in turn, determine when the topology of a zero set changes. We explore these topics by creating a MATLAB program that draws A-discriminant curves for polynomials in two variables with five terms. The program finds all discriminant chambers and automatically computes the topology of the zero set of any bivariate pentanomials. This automatic topology computation for high degree polynomials will be quite useful for the real algebraic geometry community.