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OverviewThe authors prove an elementary recursive bound on the degrees for Hilbert's 17th problem. More precisely they express a nonnegative polynomial as a sum of squares of rational functions and obtain as degree estimates for the numerators and denominators the following tower of five exponentials $ 2^{ 2^{ 2^{d^{4^{k}}} } } $ where $d$ is the number of variables of the input polynomial. The authors' method is based on the proof of an elementary recursive bound on the degrees for Stengle's Positivstellensatz. More precisely the authors give an algebraic certificate of the emptyness of the realization of a system of sign conditions and obtain as degree bounds for this certificate a tower of five exponentials, namely $ 2^{ 2^{\left(2^{\max\{2,d\}^{4^{k}}}+ s^{2^{k}}\max\{2, d\}^{16^{k}{\mathrm bit}(d)} \right)} } $ where $d$ is a bound on the degrees, $s$ is the number of polynomials and $k$ is the number of variables of the input polynomials. Full Product DetailsAuthor: Henri Lombardi , Daniel Perrucci , Marie-Francoise RoyPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.252kg ISBN: 9781470441081ISBN 10: 147044108 Pages: 113 Publication Date: 30 April 2020 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsIntroduction Weak inference and weak existence Intermediate value theorem Fundamental theorem of algebra Hermite's theory Elimination of one variable Proof of the main theorems Bibliography/References.ReviewsAuthor InformationHenri Lombardi, Universite de Franche-Comte, Besancon, France Daniel Perrucci, Universidad de Buenos Aires, Argentina Marie-Francoise Roy, Universite de Rennes, France Tab Content 6Author Website:Countries AvailableAll regions |
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