An Algorithm for Computing the Complete Root Classification of a Parametric Polynomial

摘要

The Complete Root Classification for a univariate polynomial with symbolic coefficients is the collection of all the possible cases of its root classification, together with the conditions its coefficients should satisfy for each case. Here an algorithm is given for the automatic computation of the complete root classification of a polynomial with complex symbolic coefficients. The application of complete root classifications to some real quantifier elimination problems is also described.