An elementary recursive bound for effective positivstellensatz and Hilbert's 17th problem / Henri Lombardi, Daniel Perrucci, Marie-Françoise Roy.

Format:

Book

Author/Creator:

Lombardi, Henri, author.

Perrucci, Daniel, author.

Roy, M.-F. (Marie-Françoise), author.

Series:

Memoirs of the American Mathematical Society ; v. 1277.

Memoirs of the American Mathematical Society, 1947-6221 ; v. 1277

Language:

English

Subjects (All):

Polynomials.

Algebraic fields.

Recursive functions.

Physical Description:

1 online resource (pages cm.)

Place of Publication:

Providence, RI : American Mathematical Society, 2020.

System Details:

Mode of access : World Wide Web

text file

Summary:

"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-- Provided by publisher.

Contents:

Chapter 1. Introduction Chapter 2. Weak inference and weak existence Chapter 3. Intermediate value theorem Chapter 4. Fundamental theorem of algebra Chapter 5. Hermite's Theory Chapter 6. Elimination of one variable Chapter 7. Proof of the main theorems Chapter 8. Annex

Notes:

Includes bibliographical references.

Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2020

Description based on print version record.

Other Format:

Print version: Lombardi, Henri, elementary recursive bound for effective positivstellensatz and Hilbert's 17th problem /

ISBN:

9781470456627

Access Restriction:

Restricted for use by site license.