B.: Constructing fewer open cells by gcd computation in cad projection

A new projection operator of cylindrical algebraic decompo-sition (CAD) is proposed. The new operator computes the intersection of projection factor sets produced by different CAD projection orders. In other words, it computes the gcd of projection polynomials in the same variables produced by different CAD projection orders. We prove that the new op-erator still guarantees obtaining at least one sample point from every connected component of the highest dimension. In general, the gcd computation produces smaller projection factor sets and thus fewer open cells. Some examples that are difficult to be solved by existing tools have been worked out efficiently by our program based on the new operator. Categories and Subject Descriptors G.4 [Mathematics of computation]: Mathematical soft-ware — Algorithm design and analysi