Session S34 - Symbolic and Numerical Computation with Polynomials

Wednesday, July 14, 14:00 ~ 14:30 UTC-3

Computing efficiently the non-properness set of polynomial maps on the plane

Elias Tsigaridas

Inria Paris, France   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We present new mathematical and computational tools to develop a complete and efficient algorithm for computing the set of non-properness of (dominant) polynomial maps in the complex (and the real) plane. The set of non-properness is a subset of the plane where a dominant polynomial map is not proper. The algorithm takes into account the sparsity of polynomials as it depends on their Newton polytopes. As a byproduct it also provides a representation of the set of non-properness as a union of algebraic or semi-algebraic sets, that correspond to edges of the Newton polytopes.

Joint work with Boulos El Hilany (TU Braunschweig, Germany).

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