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Quantitative Fundamental Theorem of Algebra

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Quantitative Fundamental Theorem of Algebra

Using subresultants, we modify a recent 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 requested to hold for real polynomials of degree at most d^2. We also explain that the classical algebraic proof due to Laplace requires [IVT] for real polynomials of exponential degree. These quantitative results highlight the difference in nature of these two proofs.

- Séminaire Géométrie et théorie des modèles

Détails :

Orateur / Oratrice : Marie-Françoise Roy
Date : 31 janvier 2020
Horaire : 14h15 - 15h35
Lieu : ENS Salle W