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Session S34 - Symbolic and Numerical Computation with Polynomials

Wednesday, July 21, 18:45 ~ 19:15 UTC-3

Smooth Points on Semi-algebraic sets

Agnes Szanto

North Carolina State University, United States   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Many algorithms for determining properties of real algebraic or semi-algebraic sets rely upon the ability to compute smooth points. In this talk, I present a simple procedure based on computing the critical points of some well-chosen function that guarantees the computation of smooth points in each connected bounded component of a real atomic semi-algebraic set. Our technique is intuitive in principal, performs well on previously difficult examples, and is straightforward to implement using existing numerical algebraic geometry software. I also present the application of our method to design an efficient algorithm to compute the real dimension of algebraic sets, the original motivation for this research.

Joint work with Katherine Harris (North Carolina State University) and Jonathan Hauenstein (University of Notre Dame).

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