Includes bibliographical references (p. [393]-418) and index.

A.Dickenstein, I.Z.Emiris: Preface.- 1 E.Cattani, A.Dickenstein: Introduction to Residues and Resultants.- 2 D.A.Cox: Solving Equations via Algebras.- 3 M.Elkadi, B.Mourrain: Symbolic-numeric Methods for Solving Polynomial Equations and Applications.- 4 A.Kehrein, M.Kreuzer, L.Robbiano: An Algebraist's View on Border Bases.- 5 M.Stillman: Tools for Computing primary Decompositions and Applications to Ideals Associated to Bayesian Networks.- 6 J.Sabia: Algorithms and Their Complexities.- 7 I.Z.Emiris: Toric Resultants and Applications to Geometric Modelling.- 8 A.J.Sommese, J.Verschelde, Ch.W.Wampler: Introduction to Numerical Algebraic Geometry.- 9 G.Cheze, A.Galligo: Four Lectures on Polynomial Absolute Factorization.- References.- Index.

This book provides a general introduction to modern mathematical aspects in computing with multivariate polynomials and in solving algebraic systems. It presents the state of the art in several symbolic, numeric, and symbolic-numeric techniques, including effective and algorithmic methods in algebraic geometry and computational algebra, complexity issues, and applications ranging from statistics and geometric modelling to robotics and vision.Graduate students, as well as researchers in related areas, will find an excellent introduction to currently interesting topics. These cover Groebner and border bases, multivariate resultants, residues, primary decomposition, multivariate polynomial factorization, homotopy continuation, complexity issues, and their applications.