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

Let <i>V</i> ⊂ R<sup><i>r</i></sup> denote the real algebraic variety defined by the conjunction <i>f</i> = 0 ∧ <i>g</i> = 0, where <i>f</i> and <i>g</i> are real polynomials in the variables <i>x</i><sub>1</sub>, ..., <i>x</i><sub><i>r</i></sub> and let <i>S</i> be a submanifold of R<sup><i>r</i>-2</sup>. This paper proposes the notion of the <i>analytic delineability of V on S with respect to the last 2 variables</i>. It is suggested that such a notion could be useful in solving more efficiently certain quantifier elimination problems which contain the conjunction <i>f</i> = 0 ⊂ <i>g</i> = 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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