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 › peer-review

9 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

Access to Document

10.1016/j.jsc.2015.02.001

Link to publication in Scopus

Cite this

@article{d34a91e8b570467aaf492b33ee36d72b,

title = "On using Lazard's projection in CAD construction",

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.",

keywords = "cylindrical algebraic decomposition, projection operation, theorem of Abhyankar and Jung",

author = "Scott McCallum and Hoon Hong",

year = "2016",

month = jan,

doi = "10.1016/j.jsc.2015.02.001",

language = "English",

volume = "72",

pages = "65--81",

journal = "Journal of Symbolic Computation",

issn = "0747-7171",

publisher = "ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD",

}

TY - JOUR

T1 - On using Lazard's projection in CAD construction

AU - McCallum, Scott

AU - Hong, Hoon

PY - 2016/1

Y1 - 2016/1

N2 - 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.

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.

KW - cylindrical algebraic decomposition

KW - projection operation

KW - theorem of Abhyankar and Jung

UR - http://www.scopus.com/inward/record.url?scp=84937524270&partnerID=8YFLogxK

U2 - 10.1016/j.jsc.2015.02.001

DO - 10.1016/j.jsc.2015.02.001

M3 - Article

AN - SCOPUS:84937524270

VL - 72

SP - 65

EP - 81

JO - Journal of Symbolic Computation

JF - Journal of Symbolic Computation

SN - 0747-7171

ER -

On using Lazard's projection in CAD construction

Abstract

Keywords

Access to Document

Fingerprint

Cite this