On delineability of varieties in CAD-based quantifier elimination with two equational constraints

Scott McCallum*, Christopher W. Brown

*Corresponding author for this work

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

5 Citations (Scopus)

Abstract

Let V ⊂ ℝr denote the real algebraic variety defined by the conjunction f = 0 ∧ g = 0, where f and g are real polynomials in the variables x1, ..., xr and let S be a submanifold of ℝr-2. This paper proposes the notion of the analytic delineability of V on S with respect to the last 2 variables. It is suggested that such a notion could be useful in solving more efficiently certain quantifier elimination problems which contain the conjunction f = 0 ∧ g = 0 as subformula, using a variation of the CAD-based method. Two bi-equational lifting theorems are proved which provide the basis for such a method.

Original languageEnglish
Title of host publicationProceedings of the 2009 International Symposium on Symbolic and Algebraic Computation, ISSAC 2009
EditorsJohn P. May
Place of PublicationNew York
PublisherAssociation for Computing Machinery (ACM)
Pages71-78
Number of pages8
ISBN (Print)9781605586090
DOIs
Publication statusPublished - 2009
Event2009 International Symposium on Symbolic and Algebraic Computation, ISSAC 2009 - Seoul, Korea, Republic of
Duration: 28 Jul 200931 Jul 2009

Other

Other2009 International Symposium on Symbolic and Algebraic Computation, ISSAC 2009
CountryKorea, Republic of
CitySeoul
Period28/07/0931/07/09

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    McCallum, S., & Brown, C. W. (2009). On delineability of varieties in CAD-based quantifier elimination with two equational constraints. In J. P. May (Ed.), Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation, ISSAC 2009 (pp. 71-78). New York: Association for Computing Machinery (ACM). https://doi.org/10.1145/1576702.1576715