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when quoting this document, please refer to the following
URN: urn:nbn:de:0030-drops-2763
URL: http://drops.dagstuhl.de/opus/volltexte/2006/276/
Mahboubi, Assia

Programming and certifying a CAD algorithm in the Coq system

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Abstract

A. Tarski has shown in 1948 that one can perform quantifier elimination in the theory of real closed fields. The introduction of the Cylindrical Algebraic Decomposition (CAD) method has later allowed to design rather feasible algorithms. Our aim is to program a reflectional decision procedure for the Coq system, using the CAD, to decide whether a (possibly multivariate) system of polynomial inequalities with rational coefficients has a solution or not. We have therefore implemented various computer algebra tools like gcd computations, subresultant polynomial or Bernstein polynomials.

BibTeX - Entry

@InProceedings{mahboubi:DSP:2006:276,
  author =	{Assia Mahboubi},
  title =	{Programming and certifying a CAD algorithm in the Coq system},
  booktitle =	{Mathematics, Algorithms, Proofs},
  year =	{2006},
  editor =	{Thierry Coquand and Henri Lombardi and Marie-Fran{\c{c}}oise Roy},
  number =	{05021},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Internationales Begegnungs- und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2006/276},
  annote =	{Keywords: Computer algebra, Bernstein polynomials, subresultants, CAD, Coq, certification.}
}

Keywords: Computer algebra, Bernstein polynomials, subresultants, CAD, Coq, certification.
Seminar: 05021 - Mathematics, Algorithms, Proofs
Documenttype: InProceedings
Issue date: 2006
Date of publication: 16.01.2006

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