и вот еще такой текст
https://www.math.ens.fr/~benoist/articles/CarresEMS.pdf
(Oliver Benoist. Writing Positive Polynomials as Sums of (Few) Squares)

«In 1927, Artin proved that a real polynomial that is positive semidefinite is a sum of squares of rational functions, thus solving Hilbert’s 17th problem. We review Artin’s Theorem and its posterity, browsing through basic examples, classical results and recent developments. We focus on a question first considered by Pfister: can one write a positive semidefinite polynomial as a sum of few squares?