An Incremental Algorithm for Computing Cylindrical Algebraic Decompositions

  • Changbo ChenEmail author
  • Marc Moreno MazaEmail author
Conference paper


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.


Polynomial System Incremental Algorithm Triangular Decomposition Quantifier Elimination Cylindrical System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



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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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Chongqing Key Laboratory of Automated Reasoning and CognitionChongqing Institute of Green and Intelligent Technology, Chinese Academy of SciencesChongqingChina
  2. 2.ORCCAUniversity of Western OntarioLondonCanada

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