Proceedings of Symposia in Applied Mathematics 1998; 172 pp; hardcover Volume: 53 ISBN10: 0821807501 ISBN13: 9780821807507 List Price: US$43 Member Price: US$34.40 Order Code: PSAPM/53
 This book introduces readers to key ideas and applications of computational algebraic geometry. Beginning with the discovery of Gröbner 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 Gröbner bases and resultants, then discusses some of the more recent methods for solving systems of polynomial equations. A sampler of possible applications follows, including computeraided geometric design, complex information systems, integer programming, and algebraic coding theory. The lectures in the book assume no previous acquaintance with the material. Readership Graduate students and research mathematicians interested in commutative rings and algebras. Table of Contents  D. A. Cox  Introduction to Gröbner bases
 B. Sturmfels  Introduction to resultants
 D. Manocha  Numerical methods for solving polynomial equations
 T. W. Sederberg  Applications to computer aided geometric design
 X. H. Kramer and R. C. Laubenbacher  Combinatorial homotopy of simplicial complexes and complex information systems
 R. R. Thomas  Applications to integer programming
 J. B. Little  Applications to coding theory
 Index
