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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 on all the real roots of f if and only if g is a sum of squares of rational polynomials modulo f.
Über die Darstellung definiter Funktionen durch Quadrate
Edmund Landau · 1906
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Sur la représentation en somme de carrés des polynômes à une indéterminée sur un corps de nombres algébriques
Y. Pourchet · 1971
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Positive polynomials on compact semi-algebraic sets
Mihai Putinar · 1993
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An explicit construction of distinguished representations of polynomials nonnegative over finite sets
Pablo A. Parrilo · 2002
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Erich Kaltofen, Bin Li, Zhengfeng Yang, and Lihong Zhi · 2008
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Victor Magron, Mohab Safey El Din, and Markus Schweighofer · 2019
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Victor Magron, Mohab Safey El Din, and Trung-Hieu Vu · 2021
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Victor Magron and Mohab Safey El Din · 2021
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Victor Magron, Mohab Safey El Din, Markus Schweighofer, and Trung Hieu Vu · 2022
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Sums of squares of polynomials with rational coefficients
Claus Scheiderer · 2016
Cited alongside, same era.