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arXiv · 2112.00490

Univariate Rational Sums of Squares

Teresa Krick·Bernard Mourrain·Agnes Szanto
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Abstract

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 on 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 on the real roots of a non-zero polynomial f , when the above assumption is satisfied.

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Teresa Krick, Bernard Mourrain, Agnes Szanto. 2022-04-12. Univariate Rational Sums of Squares. https://doi.org/10.33044/revuma.2904

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