Titlebook: Solving Polynomial Equations; Foundations, Algorit Manuel Bronstein,Arjeh M. Cohen,Ioannis Z. Emiris Textbook 2005 Springer-Verlag Berlin H

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,An algebraist’s view on border bases,. The first and higher borders of . can be used to measure the distance of a term from . and to define .-border bases. We study their existence and uniqueness, their relation to Gr?bner bases, and their characterization in terms of commuting matrices. Finally, we use border bases to solve a problem

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Algorithms and their complexities,ms solving polynomial equation systems. Although it is essentially self-contained, many of the definitions, problems and results we deal with also appear in many other chapters of this book. We start by considering algorithms which use the dense representation of multivariate polynomials. Some resul

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Toric resultants and applications to geometric modelling,asic objects are the Newton polytope of a polynomial, the Minkowski sum of a set of convex polytopes, and a mixed polyhedral subdivision of such a Minkowski sum. Different matrices expressing the toric resultant shall be discussed, and effective methods for their construction will be described based

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