Revista de la
Unión Matemática Argentina
Univariate rational sums of squares
Teresa Krick, Bernard Mourrain, and Agnes Szanto
Volume 64, no. 2 (2022), pp. 215–237

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Given rational univariate polynomials $f$ and $g$ such that $\gcd (f,g)$ and $f/\gcd(f,g)$ are relatively prime, we show that $g$ is non-negative at all the real roots of $f$ if and only if $g$ is a sum of squares of rational polynomials modulo $f$. We complete our study by exhibiting an algorithm that produces a certificate that a polynomial $g$ is non-negative at the real roots of a non-zero polynomial $f$ when the above assumption is satisfied.


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