On using Lazard's projection in CAD construction

Scott McCallum, Hoon Hong

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


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 languageEnglish
Pages (from-to)65-81
Number of pages17
JournalJournal of Symbolic Computation
Publication statusPublished - Jan 2016


  • cylindrical algebraic decomposition
  • projection operation
  • theorem of Abhyankar and Jung


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