Solving Polynomial Equations Foundations Algorithms And Applications Alicia Dickenstein Ioannis Z Emiris Eds by Alicia Dickenstein; Ioannis Z Emiris (eds.) 9783540243267, 3540243267 instant download after payment.

The subject of this book is the solution of polynomial equations, that is, systems of (generally) non-linear algebraic equations. This study is at the heart of several areas of mathematics and its applications. It has provided the motivation for advances in different branches of mathematics such as algebra, geometry, topology, and numerical analysis. In recent years, an explosive development of algorithms and software has made it possible to solve many problems which had been intractable up to then and greatly expanded the areas of applications to include robotics, machine vision, signal processing, structural molecular biology, computer-aided design and geometric modelling, as well as certain areas of statistics, optimization and game theory, and biological networks. At the same time, symbolic computation has proved to be an invaluable tool for experimentation and conjecture in pure mathematics. As a consequence, the interest in effective algebraic geometry and computer algebra has extended well beyond its original constituency of pure and applied mathematicians and computer scientists, to encompass many other scientists and engineers. While the core of the subject remains algebraic geometry, it also calls upon many other aspects of mathematics and theoretical computer science, ranging from numerical methods, differential equations and number theory to discrete geometry, combinatorics and complexity theory. The goal of this book is to provide a general introduction to modern mathematical aspects in computing with multivariate polynomials and in solving algebraic systems.