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Journal Articles Revista de la Unión Matemática Argentina Year : 2022

Univariate Rational Sums of Squares

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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Dates and versions

hal-03442193 , version 1 (23-11-2021)
hal-03442193 , version 2 (11-04-2022)

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Cite

Teresa Krick, Bernard Mourrain, Agnes Szanto. Univariate Rational Sums of Squares. Revista de la Unión Matemática Argentina, 2022, 64 (2), pp.215-237. ⟨10.33044/revuma.2904⟩. ⟨hal-03442193v2⟩
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