to residues and resultants.- Solving equations via algebras.- Symbolic-numeric methods for solving polynomial equations and applications.- An algebraist’s view on border bases.- Tools for computing primary decompositions and applications to ideals associated to Bayesian networks.- Algorithms and their complexities.- Toric resultants and applications to geometric modelling.- to numerical algebraic geometry.- Four lectures on polynomial absolute factorization.
From the reviews of the first edition: "[...] The editors of the book — Alicia Dickenstein and Ioannis Emiris — have done a very good job in collecting a set of expository lectures on a very interesting branch of mathematics. I imagine that this book will be of use to anyone working in the area, and would be a good introduction for a graduate student or someone wishing to start working in the field. [...]" Darren Glass, MAA Review, January 2006 "Dieses Buch besteht aus neun weitgehend unabhängigen Kapiteln zum Thema "Lösung polynomialer Gleichungssysteme", geschrieben von bekannten Experten. Der Schwerpunkt liegt auf spezialisierten Themen, bei denen in jüngerer Zeit beachtliche Fortschritte erzielt wurden. Es gibt deshalb wenig Überschneidungen mit anderen Büchern der Computeralgebra. [...] Insgesamt ist dieses Buch eine reiche Quelle von Informationen und eine sehr willkommene Ergänzung zu den bereits vorhandenen Lehrbüchern im Bereich der Lösung polynomialer Gleichungssysteme. Es sollte in keinem Regal fehlen." Peter Bürgisser, Computeralgebra, Ausgabe 39, Oktober 2006 "Although about 15 authors have contributed to this book it constitutes a unified whole. Its subjects are the diverse methods, techniques and algorithms in solving multivariate (non-linear) polynomial equations or systems of them, which mostly have been developed in recent years. … All in all there is presented a detailed account, which often leads to the front of research." (G. Kowol, Monatshefte für Mathematik, Vol. 148 (4), 2006)
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