On using Lazard's projection in CAD construction. (January 2016)

• Record Type: Journal Article
• Authors: McCallum, Scott; Hong, Hoon
• Is Part Of: Journal of symbolic computation. Volume 72(2016)
• Page Start: 65
• Page End: 81
• Publication Date: 2016-01
• Subjects: Cylindrical algebraic decomposition -- Projection operation -- Theorem of Abhyankar and Jung; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2015.02.001
• Languages: English
• ISSNs: 0747-7171

Abstract

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.