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Using algebraic geometry / David Cox, John Little, Donald O'Shea

Main Author Cox, David A. Coauthor Little, John B.
O'Shea, Donald
Country Estados Unidos. Publication New York : Springer, cop.1998 Description XII, 499 p. : il. ; 24 cm Series Graduate texts in mathematics , 185 ISBN 0-387-98492-5 CDU 512.7
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Item type Current location Call number Status Date due Barcode Item holds
Monografia Biblioteca Geral da Universidade do Minho
BGUM 512.7 - C Available 238065
Total holds: 0

Enhanced descriptions from Syndetics:

In recent years, the discovery of new algorithms for dealing with polynomial equations, coupled with their implementation on inexpensive yet fast computers, has sparked a minor revolution in the study and practice of algebraic geometry.

Reviews provided by Syndetics


Many mathematics subjects show two faces: one speaks only to very special, well-behaved objects, objects sufficiently small, symmetrical, extreme, smooth, whatever; concerning such mathematical VIPs one hopes to make statements both delicate and refined. The other face speaks to anything that walks in off the street; and, at great cost, answers questions only of a crude nature but in a fully general context, often using algorithms and machine computation. Until recently, nearly all exposition of algebraic geometry revealed only the first side of the subject, concentrating on varieties only of low dimension, usually just curves and surfaces, or those connected with algebraic groups. Recently, powerful algorithms have emerged, especially those dealing with Grobner bases, and these allow one to answer questions about ideals generated by arbitrary sets of polynomials, hence about varieties defined by arbitrary sets of equations. With such powerful algorithms, mathematicians now find it profitable to encode in algebraic terms certain problems from outside algebraic geometry. Cox, Little, and O'Shea develop this side of algebraic geometry and demonstrate such applications as volumes of convex polytopes, integer programming, and error-correcting codes. Their tack runs orthogonally to other expositions; e.g., they treat Goppa codes by a novel approach, avoiding classical curve theory, Riemann-Roch, Jacobian varieties, etc. A book both appealing and unique, it can either stand on its own or serve as an antidote to more abstract treatments (e.g., to demystify cohomology). A distant cousin, Boissonat and Yvinec's Algorithmic Geometry, collects recipes for analyzing linear and piecewise linear objects using tools from modern computer science set forth in the first part of the book. Special topics treated include convex hulls, triangulations, hyperplane arrangements, and Voronoi diagrams (a tool related to packings) in both Euclidean and non-Euclidean spaces. Half text, half handbook, this book offers a picture of the state-of-the-art, but also invites readers to jump in wherever they see something interesting or useful. Highly recommended. Upper-division undergraduates and up. D. V. Feldman University of New Hampshire

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