Applications of computational algebraic geometry : American Mathematical Society short course, January 6-7, 1997, San Diego, California
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Bibliographic Information
Applications of computational algebraic geometry : American Mathematical Society short course, January 6-7, 1997, San Diego, California
（Proceedings of symposia in applied mathematics, v. 53 . AMS short course lecture notes）
American Mathematical Society, c1998
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Note
Includes bibliographical references and index
"Lecture notes prepared for the American Mathematical Society Short Course, Applications of Computational Algebraic Geometry" -- T.p. verso
Description and Table of Contents
Description
This book introduces readers to key ideas and applications of computational algebraic geometry. Beginning with the discovery of Grobner bases and fueled by the advent of modern computers and the rediscovery of resultants, computational algebraic geometry has grown rapidly in importance. The fact that 'crunching equations' is now as easy as 'crunching numbers' has had a profound impact in recent years. At the same time, the mathematics used in computational algebraic geometry is unusually elegant and accessible, which makes the subject easy to learn and easy to apply. This book begins with an introduction to Grobner bases and resultants, then discusses some of the more recent methods for solving systems of polynomial equations. A sampler of possible applications follows, including computer-aided geometric design, complex information systems, integer programming, and algebraic coding theory. The lectures in the book assume no previous acquaintance with the material.
Table of Contents
Introduction to Grobner bases by D. A. Cox Introduction to resultants by B. Sturmfels Numerical methods for solving polynomial equations by D. Manocha Applications to computer aided geometric design by T. W. Sederberg Combinatorial homotopy of simplicial complexes and complex information systems by X. H. Kramer and R. C. Laubenbacher Applications to integer programming by R. R. Thomas Applications to coding theory by J. B. Little Index.
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