Since a real univariate polynomial does not always have real roots, a very natural
algorithmic problem, is to design a method to count the number of real roots of a given …

This paper has two parts. In the first part we give a simple and constructive proof that
quantifier elimination in real algebra is doubly exponential, even when there is only one free …

This chapter describes a number of results obtained in the last sixty years in the theory of
non-zero-sum discrete-time stochastic games. We overview almost all basic streams of …

" Constraints, such as linear or polynomial equalities, are used to finitely represent possibly
infinite sets of points. They provide an elegant way to combine classical relational data with …

Optimization Theory is becoming a more and more important mathematical as well as
interdisciplinary area, especially in the interplay between mathematics and many other …

This book is mainly devoted to some computational and algorithmic problems in finite fields
such as, for example, polynomial factorization, finding irreducible and primitive polynomials …

H=-A+ V,(1.1) where A is the discrete Laplacian on Z d and V a potential, plays a central role
in quanturn mechanics. Starting with the seminal paper by P. Anderson [2], many works …

A quantifier elimination algorithm by cylindrical algebraic decomposition based on regular
chains is presented. The main idea is to refine a complex cylindrical tree until the signs of …

Introduced forty years ago, relational databases proved unusually successful and durable.
However, relational database systems were not designed for modern applications and …

We study a basic algorithmic problem in algebraic geometry, which we call NNL, of
constructing a normalizing map as per Noether's Normalization Lemma. For general explicit …