Triangular decomposition of semi-algebraic systems

  • Authors:

  • Changbo Chen;James H. Davenport;John P. May;Marc Moreno Maza;Bican Xia;Rong Xiao

  • Affiliations:

  • University of Western Ontario;University of Bath;Maplesoft;University of Western Ontario;Peking University;University of Western Ontario

  • Venue:
  • Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
  • Year:
  • 2010

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Abstract

Regular chains and triangular decompositions are fundamental and well-developed tools for describing the complex solutions of polynomial systems. This paper proposes adaptations of these tools focusing on solutions of the real analogue: semi-algebraic systems. We show that any such system can be decomposed into finitely many regular semi-algebraic systems. We propose two specifications of such a decomposition and present corresponding algorithms. Under some assumptions, one type of decomposition can be computed in singly exponential time w.r.t. the number of variables. We implement our algorithms and the experimental results illustrate their effectiveness.