Polynomials in $\mathbb {R}[x,y]$ that are sums of squares in $\mathbb {R}(x,y)$

DOI10.1090/S0002-9939-01-05927-5zbMath0972.12003MaRDI QIDQ2731900

David B. Leep, Colin L. Starr

Publication date: 30 July 2001

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

sum of squares of polynomialspositive semidefinite polynomial

Mathematics Subject Classification ID

Sums of squares and representations by other particular quadratic forms (11E25) Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) (12D15)

Related Items (4)

Sums of three squares and Noether–Lefschetz loci ⋮ Positivity certificates and polynomial optimization on non-compact semialgebraic sets ⋮ Exact certification in global polynomial optimization via sums-of-squares of rational functions with rational coefficients ⋮ Estimates of the Pythagoras number of \(\mathbb R_m[x_1, \ldots , x_n\) through lattice points and polytopes]

Cites Work

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• Sums of squares in some integral domains
• Positive definite rational functions of two variables which are not the sum of three squares
• On sums of squares and on elliptic curves over function fields
• Zur Darstellung definiter Funktionen als Summe von Quadraten. (To the representation of definite functions as the sum of squares)
• A remark on the quadratic analogue of the Quillen-Suslin theorem.
• Modules and Quadratic Forms over Polynomial Algebras

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