DISCOVERER : A tool for solving problems involving polynomial inequalities ∗

discoverer, developed under Maple, is a package aiming at discovering and proving inequality-type theorems. It can discover new inequalities automatically, without requiring us to put forward any conjectures beforehand. It is also applied to the classification of the real physical solutions of geometric constraint problems. Many inequalities with various backgrounds have been discovered or re-discovered by the package. Furthermore, discoverer also has many other functions for solving problems related to real algebra and geometry such as, computing the number of distinct real solutions of a system of polynomial equations and inequalities and, determining whether or not a polynomial is semi-definite under some constraints of polynomial inequalities.