Sums of squares of polynomials with rational coefficients

DOI10.4171/JEMS/620zbMath1354.14036arXiv1209.2976MaRDI QIDQ726755

Claus Scheiderer

Publication date: 14 July 2016

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1209.2976

zbMATH Keywords

Hilbert's 17th problemreal plane quarticssums of squares with rational coefficients

Mathematics Subject Classification ID

Sums of squares and representations by other particular quadratic forms (11E25) Rational points (14G05) Hypersurfaces and algebraic geometry (14J70) Real algebraic and real-analytic geometry (14P99)

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Cites Work

• Sums of squares on the hypercube
• Tight bounds for rational sums of squares over totally real fields
• Handbook on semidefinite, conic and polynomial optimization
• Exact certification in global polynomial optimization via sums-of-squares of rational functions with rational coefficients
• Computing Rational Points in Convex Semialgebraic Sets and Sum of Squares Decompositions
• Hilbert’s theorem on positive ternary quartics: A refined analysis
• Sums of squares over totally real fields are rational sums of squares
• THE TOPOLOGY OF REAL PROJECTIVE ALGEBRAIC VARIETIES
• Sums of squares of linear forms
• Handbook of semidefinite programming. Theory, algorithms, and applications
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