Session S34 - Symbolic and Numerical Computation with Polynomials

Wednesday, July 21, 16:30 ~ 17:00 UTC-3

Sign conditions for the existence of at least one positive solution of a sparse polynomial system

Alicia Dickenstein

Universidad de Buenos Aires, Argentina   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We give sign conditions on the support and coefficients of a sparse system of d generalized polynomials in d variables that guarantee the existence of at least one positive real root, based on degree theory and Gale duality. In the case of integer exponents, we relate our sufficient conditions to algebraic conditions that emerged in the study of toric ideals.

Joint work with Frédéric Bihan (Université Savoie Mont Blanc) and Magalí Giaroli (Universidad de Buenos Aires).

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