English

An elementary recursive bound for effective Positivstellensatz and Hilbert 17-th problem

Algebraic Geometry 2017-04-12 v3

Abstract

We prove elementary recursive bounds in the degrees for Positivstellensatz and Hilbert 17-th problem, which is the expression of a nonnegative polynomial as a sum of squares of rational functions. We obtain a tower of five exponentials. A precise bound in terms of the number and degree of the polynomials and their number of variables is provided in the paper.

Keywords

Cite

@article{arxiv.1404.2338,
  title  = {An elementary recursive bound for effective Positivstellensatz and Hilbert 17-th problem},
  author = {Henri Lombardi and Daniel Perrucci and Marie-Françoise Roy},
  journal= {arXiv preprint arXiv:1404.2338},
  year   = {2017}
}
R2 v1 2026-06-22T03:46:31.388Z