Solving Systems of Polynomial Equations (CBMS Regional Conference Series in Mathematics 97)

Bernd Sturmfels

ISBN 10: 0821832514 / ISBN 13: 9780821832516

Published by American Mathematical Society, 2002

About this Item

*Price HAS BEEN REDUCED by 10% until Monday, Aug. 25 (weekend SALE item)* 152 pp., Paperback, previous owner's name to the front free endpaper, a few pages creased at the fore edge, else very good. - If you are reading this, this item is actually (physically) in our stock and ready for shipment once ordered. We are not bookjackers. Buyer is responsible for any additional duties, taxes, or fees required by recipient's country.

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Bibliographic Details

• Title: Solving Systems of Polynomial Equations (CBMS Regional Conference Series in Mathematics 97)
• Publisher: American Mathematical Society
• Publication Date: 2002
• Language: English
• ISBN 10: 0821832514
• ISBN 13: 9780821832516
• Binding: Soft cover
• Condition: Very Good

About this title

Synopsis

A classic problem in mathematics is solving systems of polynomial equations in several unknowns. Today, polynomial models are ubiquitous and widely used across the sciences. They arise in robotics, coding theory, optimization, mathematical biology, computer vision, game theory, statistics, and numerous other areas. <P>This book furnishes a bridge across mathematical disciplines and exposes many facets of systems of polynomial equations. It covers a wide spectrum of mathematical techniques and algorithms, both symbolic and numerical. <P>The set of solutions to a system of polynomial equations is an algebraic variety--the basic object of algebraic geometry. The algorithmic study of algebraic varieties is the central theme of computational algebraic geometry. Exciting recent developments in computer software for geometric calculations have revolutionized the field. Formerly inaccessible problems are now tractable, providing fertile ground for experimentation and conjecture. <P>The first half of the book gives a snapshot of the state of the art of the topic. Familiar themes are covered in the first five chapters, including polynomials in one variable, Gröbner bases of zero-dimensional ideals, Newton polytopes and Bernstein's Theorem, multidimensional resultants, and primary decomposition. <P>The second half of the book explores polynomial equations from a variety of novel and unexpected angles. It introduces interdisciplinary connections, discusses highlights of current research, and outlines possible future algorithms. Topics include computation of Nash equilibria in game theory, semidefinite programming and the real Nullstellensatz, the algebraic geometry of statistical models, the piecewise-linear geometry of valuations and amoebas, and the Ehrenpreis-Palamodov theorem on linear partial differential equations with constant coefficients. <P>Throughout the text, there are many hands-on examples and exercises, including short but complete sessions in Maple®, MATLAB®, Macaulay 2, Singular, PHCpack, CoCoA, and SOSTools. These examples will be particularly useful for readers with no background in algebraic geometry or commutative algebra. Within minutes, readers can learn how to type in polynomial equations and actually see some meaningful results on their computer screens. <P>Prerequisites include basic abstract and computational algebra. The book is designed as a text for a graduate course in computational algebra.