Description

Book Synopsis
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}}} } } $.

Table of Contents
  • Introduction
  • 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.

An Elementary Recursive Bound for Effective

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    RRP £75.00 – you save £7.50 (10%)

    Order before 4pm today for delivery by Tue 23 Jun 2026.

    A Paperback by Henri Lombardi, Daniel Perrucci, Marie-Francoise Roy

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      View other formats and editions of An Elementary Recursive Bound for Effective by Henri Lombardi

      Publisher: MP-AMM American Mathematical
      Publication Date: 4/30/2020 12:00:00 AM
      ISBN13: 9781470441081, 978-1470441081
      ISBN10: 147044108X

      Description

      Book Synopsis
      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}}} } } $.

      Table of Contents
      • Introduction
      • 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.

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