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Cylindrical Algebraic Decomposition I: The Basic Algorithm

  • Dennis S. Arnon
  • George E. Collins
  • Scott McCallum
Conference paper
Part of the Texts and Monographs in Symbolic Computation book series (TEXTSMONOGR)

Abstract

Given a set of r-variate integral polynomials, a cylindrical algebraic decomposition (cad) of euclidean r-space E r partitions E r into connected subsets compatible with the zeros of the polynomials. By “compatible with the zeros of the polynomials” we mean that on each subset of E r , each of the polynomials either vanishes everywhere or nowhere. For example, consider the bivariate polynomial
$${y^4} - 2{y^3} + {y^2} - 3{x^2}y + 2{x^4}.$$

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Copyright information

© Springer-Verlag/Wien 1998

Authors and Affiliations

  • Dennis S. Arnon
  • George E. Collins
  • Scott McCallum

There are no affiliations available

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