Simple Truth Invariant Cad's and Solution Formula Construction

Given a prenex formula F of elementary real algebra having k free variables, the CAD method of quantiier elimination produces a truth invariant CAD, D, for F, that is, a CAD of k-dimensional real space in each cell of which F is truth-invariant, together with an assignment to each cell of its truth value. The method also produces a set P of irreducible projection polynomials, the real zeros of which form the boundaries of the cells. Typically there exists a coarser truth-invariant CAD, D 0 , for F and a subset, P 0 , of P whose real zeros form the boundaries of D 0. We describe an eecient method for deriving such a D 0 and P 0 from D and P. The original set P may not suuce for construction of a solution formula (a quantiier-free formula equivalent to F), but P 0 will suuce if P does. We describe a method for augmenting P 0 in this case to a larger set that suuces. In either case the task of solution formula construction is much reduced by the smaller size of P 0 .