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Computational Real Algebraic Geometry in Practice (Invited Talk)

Author Hirokazu Anai



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Hirokazu Anai

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Hirokazu Anai. Computational Real Algebraic Geometry in Practice (Invited Talk). In 23rd International Conference on Rewriting Techniques and Applications (RTA'12). Leibniz International Proceedings in Informatics (LIPIcs), Volume 15, p. 1, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2012)
https://doi.org/10.4230/LIPIcs.RTA.2012.1

Abstract

Real algebraic geometry deals with the solution set of (possibly quantified) systems of polynomial equations and/or inequalities over the real numbers, which arise frequently in science and engineering. Main concern in real algebraic geometry is to determine the properties of the solution sets such as non-emptiness, dimension and quantifier free description as a semi-algebraic set. Such tasks are carried out by symbolic and algebraic algorithms:cylindrical algebraic decomposition (CAD) or quantifier elimination (QE). Various algorithms and deep complexity results about CAD and QE have been studied during the last several decades. Moreover, practically efficient software systems of QE have been developed and also are applied to many nontrivial application problems. In this talk we explain several algorithms of CAD and QE together with their engineering applications.
Keywords
  • real algebraic geometry
  • quantifier elimination
  • cylindrical algebraic decomposition
  • symbolic optimization

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