An Elementary Recursive Bound for Effective Positivstellensatz and Hilbert's 17th Problem

The 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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Lombardi, Henri
Otros Autores: Perrucci, Daniel, Roy, Marie-Françoise
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence : American Mathematical Society, 1920.
Colección:Memoirs of the American Mathematical Society Ser.
Temas:
Polynomials.
Algebraic fields.
Recursive functions.
Algebraic stacks.
Polynômes.
Corps algébriques.
Fonctions récursives.
Algebraic stacks
Algebraic fields
Polynomials
Recursive functions
Acceso en línea:Texto completo
Descripción
Sumario:The 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.
Descripción Física:1 online resource (138 pages)
ISBN:9781470456627
1470456621

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