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An Incremental Algorithm for Computing Cylindrical Algebraic Decompositions

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Computer Mathematics

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.

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Notes

  1. 1.

    More precisely, a multivariate polynomial regarded as a univariate one with respect to its main variable.

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Acknowledgments

The authors would like to thank the readers who helped to improve the earlier versions of this paper. This research was supported by the Academic Development Fund ADF-Major-27145 of The University of Western Ontario.

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Authors and Affiliations

  1. Chongqing Key Laboratory of Automated Reasoning and Cognition, Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, Chongqing, China

    Changbo Chen

  2. ORCCA, University of Western Ontario, London, Canada

    Changbo Chen & Marc Moreno Maza

Authors
  1. Changbo Chen
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  2. Marc Moreno Maza
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Corresponding authors

Correspondence to Changbo Chen or Marc Moreno Maza .

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Editors and Affiliations

  1. Academy of Mathematics & System Science, Beijing, China

    Ruyong Feng

  2. Department of Mathematics and Computer S, University of Antwerp, Antwerp, Antwerpen, Belgium

    Wen-shin Lee

  3. Department of Mathematical Information S, Tokyo University of Science, Tokyo, Tokyo, Japan

    Yosuke Sato

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Chen, C., Moreno Maza, M. (2014). An Incremental Algorithm for Computing Cylindrical Algebraic Decompositions. In: Feng, R., Lee, Ws., Sato, Y. (eds) Computer Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43799-5_17

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