The Cylindrical Algebraic Decomposition algorithm, in its projection phase, proceeds by eliminating one variable from a given set of polynomials V by means of the computation of ihe principal subresultant coefficients of a certain set of pairs of polynomials in P (including their derivatives and reducta). Since this method produces usually a big number of polynomials, and since the process must be iterated several times, any improvement in the projection phase would convey to dramatically speed up the efficiency of the Cylindrical Algebraic Decomposition algorithm.
The purpose of this paper is to present two approaches allowing, in some cases, to simplify the projection phase in the Cylindrical Algebraic Decomposition algorithm when some of the involved polynomials are prescribed to have a particular sign behaviour.