Finding at least one point in each connected component of a real algebraic set defined by a single equation

DOI10.1006/jcom.2000.0563zbMath1009.14010OpenAlexW2089339786MaRDI QIDQ5925972

Mohab Safey El Din, Marie-Françoise Roy, Fabrice Rouillier

Publication date: 1 April 2003

Published in: Journal of Complexity (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/d146a9d094aa939415b74c940f8208d75da23f58

zbMATH Keywords

complexityalgorithmGröbner basisrational univariate representationreal hypersurfaceSard's theoremsolving polynomial equation

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Real algebraic sets (14P05) Computational aspects of algebraic surfaces (14Q10)

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Uses Software

• FGb
• ISOLATE

Cites Work

• Quantifier elimination for real algebra -- the quadratic case and beyond
• Solving systems of polynomial inequalities in subexponential time
• Computing the conductor of an integral extension
• On the computational complexity and geometry of the first-order theory of the reals. III: Quantifier elimination
• Solving zero-dimensional systems through the rational univariate representation
• Generic computation of the real closure of an ordered field.
• A new decision method for elementary algebra
• On the Theoretical and Practical Complexity of the Existential Theory of Reals
• On the combinatorial and algebraic complexity of quantifier elimination
• Properties of Gröbner bases under specializations
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