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Record Nr. |
UNINA9910794062503321 |
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Autore |
Lombardi Henri |
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Titolo |
An elementary recursive bound for effective positivstellensatz and Hilbert's 17th problem / / Henri Lombardi, Daniel Perrucci, Marie-Françoise Roy |
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Pubbl/distr/stampa |
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Providence, Rhode Island : , : American Mathematical Society, , 2020 |
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ISBN |
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Descrizione fisica |
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1 online resource (138 pages) |
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Collana |
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Memoirs of the American Mathematical Society ; ; Volume 263 |
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Classificazione |
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Disciplina |
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Soggetti |
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Polynomials |
Algebraic fields |
Recursive functions |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references. |
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Nota di contenuto |
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Weak inference and weak existence -- Intermediate value theorem -- Fundamental theorem of algebra -- Hermite's theory -- Elimination of one variable -- Proof of the main theorems -- Annex. |
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Sommario/riassunto |
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"We prove an elementary recursive bound on the degrees for Hilbert's 17th problem. More precisely we express a nonnegative polynomial as a sum of squares of rational functions, and we obtain as degree estimates for the numerators and denominators the following tower of five exponentials 222d4k where d is the degree and k is the number of variables of the input polynomial. Our method is based on the proof of an elementary recursive bound on the degrees for Stengle's Positivstellensatz. More precisely we give an algebraic certificate of the emptyness of the realization of a system of sign conditions and we obtain as degree bounds for this certificate a tower of five exponentials, namely 2²(2max{2,d}4k+s2kmax{2,d}16kbit(d)) 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-- |
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