On using Lazard's projection in CAD construction

Scott McCallum; Hoon Hong

doi:10.1016/j.jsc.2015.02.001

On using Lazard's projection in CAD construction

Scott McCallum, Hoon Hong

Department of Computing

Research output: Contribution to journal › Article

8 Citations (Scopus)

Abstract

In 1994 Lazard proposed an improved projection operation for cylindrical algebraic decomposition (CAD). For the proof he introduced a certain notion of valuation of a multivariate Puiseux series at a point. However a gap in one of the key supporting results for the improved projection was subsequently noticed. In this paper we show that Lazard's projection is valid for CAD construction for so-called well-oriented polynomial sets. Our proof does not make use of Lazard's notion of valuation, however.

Original language	English
Pages (from-to)	65-81
Number of pages	17
Journal	Journal of Symbolic Computation
Volume	72
DOIs	https://doi.org/10.1016/j.jsc.2015.02.001
Publication status	Published - Jan 2016

Keywords

cylindrical algebraic decomposition
projection operation
theorem of Abhyankar and Jung

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10.1016/j.jsc.2015.02.001

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AB - In 1994 Lazard proposed an improved projection operation for cylindrical algebraic decomposition (CAD). For the proof he introduced a certain notion of valuation of a multivariate Puiseux series at a point. However a gap in one of the key supporting results for the improved projection was subsequently noticed. In this paper we show that Lazard's projection is valid for CAD construction for so-called well-oriented polynomial sets. Our proof does not make use of Lazard's notion of valuation, however.

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