Hilbert's seventeenth problem

Expression of polynomials as sum of squares

Hilbert's seventeenth problem is one of the 23 Hilbert problems set out in a celebrated list compiled in 1900 by David Hilbert. It concerns the expression of positive definite rational functions as sums of quotients of squares. The original question may be reformulated as:Given a multivariate polynomial that takes only non-negative values over the reals, can it be represented as a sum of squares of rational functions?

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