An Algorithm for Systems of Strong Polynomial Inequalities

Volume 4, Issue 4
Fall 1994

We describe a simplified cylindrical decomposition algorithm that allows us to find at least one rational point in each connected component of an open semialgebraic set. In particular, it allows us to decide whether a given set of strong polynomial inequalities has solutions. The algorithm does not require computations with algebraic numbers and is therefore much faster than the cylindrical decomposition.