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Problem Formulation for Truth-Table Invariant Cylindrical Algebraic Decomposition by Incremental Triangular Decomposition

  • Matthew England
  • Russell Bradford
  • Changbo Chen
  • James H. Davenport
  • Marc Moreno Maza
  • David Wilson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8543)

Abstract

Cylindrical algebraic decompositions (CADs) are a key tool for solving problems in real algebraic geometry and beyond. We recently presented a new CAD algorithm combining two advances: truth-table invariance, making the CAD invariant with respect to the truth of logical formulae rather than the signs of polynomials; and CAD construction by regular chains technology, where first a complex decomposition is constructed by refining a tree incrementally by constraint. We here consider how best to formulate problems for input to this algorithm. We focus on a choice (not relevant for other CAD algorithms) about the order in which constraints are presented. We develop new heuristics to help make this choice and thus allow the best use of the algorithm in practice. We also consider other choices of problem formulation for CAD, as discussed in CICM 2013, revisiting these in the context of the new algorithm.

Keywords

cylindrical algebraic decomposition truth table invariance regular chains triangular decomposition problem formulation 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Matthew England
    • 1
  • Russell Bradford
    • 1
  • Changbo Chen
    • 2
  • James H. Davenport
    • 1
  • Marc Moreno Maza
    • 3
  • David Wilson
    • 1
  1. 1.University of BathBathU.K.
  2. 2.Chongqing Key Laboratory of Automated Reasoning and CognitionChongqing Institute of Green and Intelligent Technology, CASChongqingChina
  3. 3.University of Western OntarioLondonCanada

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