Cylindrical algebraic decomposition by quantifier elimination

Dennis S. Arnon, Scott McCallum

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contribution

7 Citations (Scopus)

Abstract

Cylindrical algebraic decompositions were introduced as a major component of a new quantifier elimination algorithm for elementary algebra and geometry (G. Collins, 1973). In the present paper we turn the tables and show that one can use quantifier elimination for elementary algebra and geometry to obtain a new version of the cylindrical algebraic decomposition algorithm. A key part of our result is a theorem, of interest in its own right. that relates the multiplicities of the roots of a polynomial to their continuity.

Original languageEnglish
Title of host publicationComputer Algebra - EUROCAM 1982, European Computer Algebra Conference
EditorsJacques Calmet
PublisherSpringer-VDI-Verlag GmbH & Co. KG
Pages215-222
Number of pages8
ISBN (Print)9783540116073
DOIs
Publication statusPublished - 1 Jan 1982
Externally publishedYes
EventEuropean Computer Algebra Conference, EUROCAM 1982 - Marseille, France
Duration: 5 Apr 19827 Apr 1982

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume144 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

ConferenceEuropean Computer Algebra Conference, EUROCAM 1982
CountryFrance
CityMarseille
Period5/04/827/04/82

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    Arnon, D. S., & McCallum, S. (1982). Cylindrical algebraic decomposition by quantifier elimination. In J. Calmet (Ed.), Computer Algebra - EUROCAM 1982, European Computer Algebra Conference (pp. 215-222). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 144 LNCS). Springer-VDI-Verlag GmbH & Co. KG. https://doi.org/10.1007/3-540-11607-9_25