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Certificates of impossibility of Hilbert-Artin representations of a given degree for definite polynomials and functions
We deploy numerical semidefinite programming and conversion to exact rational inequalities to certify that for a positive semidefinite input polynomial or rational function, any representation as a fraction of sums-of-squares of polynomials with real coefficients must contain polynomials in the denominator of degree no less than a given input lower …