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Quantitative Fundamental Theorem of Algebra

Marie-Francoise Roy (Rennes)
Tuesday, November 12, 2019 - 16:00
Using subresultants, we modify a real-algebraic proof due to Eisermann of the Fundamental Theorem of Algebra ([FTA]) to obtain the following quantitative information: in order to prove the [FTA] for polynomials of degree d, the Intermediate Value Theorem ([IVT]) is required to hold only for real polynomials of degree at most $d^2$. We also explain that the classical proof due to Laplace requires [IVT] for real polynomials of exponential degree. These quantitative results highlight the difference in nature of these two proofs.
(Joint work with Daniel Perrucci)

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