Computing cylindrical algebraic decomposition via triangular decomposition

  • Authors:

  • Changbo Chen;Marc Moreno Maza;Bican Xia;Lu Yang

  • Affiliations:

  • University of Western Ontario, London, Canada;University of Western Ontario, London, Canada;Peking University, Beijing, China;East China Normal University, Shanghai, China

  • Venue:
  • Proceedings of the 2009 international symposium on Symbolic and algebraic computation
  • Year:
  • 2009

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Abstract

Cylindrical algebraic decomposition is one of the most important tools for computing with semi-algebraic sets, while triangular decomposition is among the most important approaches for manipulating constructible sets. In this paper, for an arbitrary finite set F ⊂ [y1,...,yn] we apply comprehensive triangular decomposition in order to obtain an F-invariant cylindrical decomposition of the n-dimensional complex space, from which we extract an F-invariant cylindrical algebraic decomposition of the n-dimensional real space. We report on an implementation of this new approach for constructing cylindrical algebraic decompositions.