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An Incremental Algorithm for Computing Cylindrical Algebraic Decompositions

In: Computer Mathematics

Author

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  • Changbo Chen

    (Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, Chongqing Key Laboratory of Automated Reasoning and Cognition
    University of Western Ontario, ORCCA)

  • Marc Moreno Maza

    (University of Western Ontario, ORCCA)

Abstract

In this paper, we propose an incremental algorithm for computing cylindrical algebraic decompositions. The algorithm consists of two parts: computing a complex cylindrical tree and refining this complex tree into a cylindrical tree in real space. The incrementality comes from the first part of the algorithm, where a complex cylindrical tree is constructed by refining a previous complex cylindrical tree with a polynomial constraint. We have implemented our algorithm in Maple. The experimentation shows that the proposed algorithm outperforms existing ones for many examples taken from the literature.

Suggested Citation

  • Changbo Chen & Marc Moreno Maza, 2014. "An Incremental Algorithm for Computing Cylindrical Algebraic Decompositions," Springer Books, in: Ruyong Feng & Wen-shin Lee & Yosuke Sato (ed.), Computer Mathematics, edition 127, pages 199-221, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-43799-5_17
    DOI: 10.1007/978-3-662-43799-5_17
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