Solving Systems of Strict Polynomial Inequalities

We present an algorithm for finding an explicit description of solution sets of systems of strict polynomial inequalities, correct up to lower dimensional algebraic sets. Such a description is sufficient for many practical purposes, such as volume integration, graphical representation of solution sets, or global optimization over open sets given by polynomial inequality constraints. Our algorithm is based on the cylindrical algebraic decomposition algorithm. It uses a simplified projection operator, and constructs only rational sample points.