An Incremental Algorithm for Computing Cylindrical Algebraic Decompositions

Changbo Chen () and Marc Moreno Maza ()
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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
Marc Moreno Maza: University of Western Ontario, ORCCA

A chapter in Computer Mathematics, 2014, pp 199-221 from Springer

Abstract: 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.

Keywords: Polynomial System; Incremental Algorithm; Triangular Decomposition; Quantifier Elimination; Cylindrical System (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-662-43799-5_17

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DOI: 10.1007/978-3-662-43799-5_17

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