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

Scott McCallum; Christopher W. Brown

doi:10.1145/1576702.1576715

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

Scott McCallum^*, Christopher W. Brown

^*Corresponding author for this work

School of Computing

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

5 Citations (Scopus)

Abstract

Let V ⊂ ℝ^r denote the real algebraic variety defined by the conjunction f = 0 ∧ g = 0, where f and g are real polynomials in the variables x₁, ..., x_r and let S be a submanifold of ℝ^r-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 language	English
Title of host publication	Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation, ISSAC 2009
Editors	John P. May
Place of Publication	New York
Publisher	Association for Computing Machinery (ACM)
Pages	71-78
Number of pages	8
ISBN (Print)	9781605586090
DOIs	https://doi.org/10.1145/1576702.1576715
Publication status	Published - 2009
Event	2009 International Symposium on Symbolic and Algebraic Computation, ISSAC 2009 - Seoul, Korea, Republic of Duration: 28 Jul 2009 → 31 Jul 2009

Other

Other	2009 International Symposium on Symbolic and Algebraic Computation, ISSAC 2009
Country/Territory	Korea, Republic of
City	Seoul
Period	28/07/09 → 31/07/09

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10.1145/1576702.1576715

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title = "On delineability of varieties in CAD-based quantifier elimination with two equational constraints",

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.",

author = "Scott McCallum and Brown, {Christopher W.}",

year = "2009",

doi = "10.1145/1576702.1576715",

language = "English",

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pages = "71--78",

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booktitle = "Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation, ISSAC 2009",

publisher = "Association for Computing Machinery (ACM)",

address = "United States",

note = "2009 International Symposium on Symbolic and Algebraic Computation, ISSAC 2009 ; Conference date: 28-07-2009 Through 31-07-2009",

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McCallum, S & Brown, CW 2009, On delineability of varieties in CAD-based quantifier elimination with two equational constraints. in JP May (ed.), Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation, ISSAC 2009. Association for Computing Machinery (ACM), New York, pp. 71-78, 2009 International Symposium on Symbolic and Algebraic Computation, ISSAC 2009, Seoul, Korea, Republic of, 28/07/09. https://doi.org/10.1145/1576702.1576715

On delineability of varieties in CAD-based quantifier elimination with two equational constraints. / McCallum, Scott; Brown, Christopher W.
Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation, ISSAC 2009. ed. / John P. May. New York: Association for Computing Machinery (ACM), 2009. p. 71-78.

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

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AB - 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.

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

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