Regular cylindrical algebraic decomposition

James Davenport; Acyr Locatelli; Gregory Sankaran

doi:10.1112/jlms.12257

Regular cylindrical algebraic decomposition

James Davenport, Acyr Locatelli, Gregory Sankaran

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Abstract

We show that a strong well-based cylindrical algebraic decomposition P of a bounded semi-algebraic set S is a regular cell decomposition, in any dimension and independently of the method by which P is constructed. Being well-based is a global condition on P that holds for the output of many widely used algorithms. We also show the same for S of dimension at most 3 and P a strong cylindrical algebraic decomposition that is locally boundary simply connected: this is a purely local extra condition.

Original language	English
Pages (from-to)	43-59
Number of pages	17
Journal	Journal of the London Mathematical Society
Volume	101
Issue number	1
Early online date	29 Jul 2019
DOIs	https://doi.org/10.1112/jlms.12257
Publication status	Published - 25 Feb 2020

Keywords

14P10 (primary)
57N99
68W30 (secondary)

ASJC Scopus subject areas

General Mathematics

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10.1112/jlms.12257

cadpaper.jlms.final.PDF
This is the peer reviewed version of the following article Davenport, J., Locatelli, A., & Sankaran, G. (2019). Regular cylindrical algebraic decomposition. Journal of the London Mathematical Society., which has been published in final form at https://doi.org/10.1112/jlms.12257. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.
Accepted author manuscript, 329 KB

https://arxiv.org/abs/1803.04029

Cite this

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Regular cylindrical algebraic decomposition

Abstract

Keywords

ASJC Scopus subject areas

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Real Geometry and Connectedness via Triangular Description

James Davenport

Gregory Sankaran

Cite this

Regular cylindrical algebraic decomposition

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

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Real Geometry and Connectedness via Triangular Description

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James Davenport

Gregory Sankaran

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