on delineability of varieties in cad-based quantifier elimination with two equational constraints
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 x 1 , ..., 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.
quantifier elimination cylindrical algebraic decomposition