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

  • Authors:

  • Scott McCallum;Christopher W. Brown

  • Affiliations:

  • Macquarie University, Sydney, Australia;United States Naval Academy, Annapolis, MD, USA

  • Venue:
  • Proceedings of the 2009 international symposium on Symbolic and algebraic computation
  • Year:
  • 2009

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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.