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

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

preprint 2014. arXiv 1404.2338

with Daniel Perrucci and Marie-Françoise Roy.
** 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.