Using Algebraic Geometry / Edition 2

Using Algebraic Geometry / Edition 2

by David A Cox, John Little, Donal O'Shea
     
 

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ISBN-10: 0387207333

ISBN-13: 9780387207339

Pub. Date: 03/17/2005

Publisher: Springer New York

In recent years, the discovery of new algorithms for dealing with polynomial equations, coupled with their implementation on fast inexpensive computers, has sparked a minor revolution in the study and practice of algebraic geometry. These algorithmic methods have also given rise to some exciting new applications of algebraic geometry. This book illustrates the many

Overview

In recent years, the discovery of new algorithms for dealing with polynomial equations, coupled with their implementation on fast inexpensive computers, has sparked a minor revolution in the study and practice of algebraic geometry. These algorithmic methods have also given rise to some exciting new applications of algebraic geometry. This book illustrates the many uses of algebraic geometry, highlighting some of the more recent applications of Gröbner bases and resultants.

The book is written for nonspecialists and for readers with a diverse range of backgrounds. It assumes knowledge of the material covered in a standard undergraduate course in abstract algebra, and it would help to have some previous exposure to Gröbner bases. The book does not assume the reader is familiar with more advanced concepts such as modules.

For the new edition, the authors have added a unified discussion of how matrices can be used to specify monomial orders; a revised presentation of the Mora normal form algorithm; two sections discussing the Gröbner fan of an ideal and the Gröbner Walk basis conversion algorithm; and a new chapter on the theory of order domains, associated codes, and the Berlekamp-Massey-Sakata decoding algorithm. They have also updated the references, improved some of the proofs, and corrected typographical errors.

David Cox is Professor of Mathematics at Amherst College. John Little is Professor of Mathematics at College of the Holy Cross. Donal O’Shea is the Elizabeth T. Kennan Professor of Mathematics and Dean of Faculty at Mt. Holyoke College. These authors also co-wrote the immensely successful book, Ideals, Varieties, and Algorithms.

Product Details

ISBN-13:
9780387207339
Publisher:
Springer New York
Publication date:
03/17/2005
Series:
Graduate Texts in Mathematics Series, #185
Edition description:
2nd ed. 2005
Pages:
575
Sales rank:
985,429
Product dimensions:
6.10(w) x 9.25(h) x 0.05(d)

Related Subjects

Table of Contents

Introduction.- Solving Polynomial Equations.- Resultants.- Computation in Local Rings.- Modules.- Free Resolutions.- Polytopes, Resultants, and Equations.- Integer Programming, Combinatorics, and Splines.- Algebraic Coding Theory.- The Berlekamp-Massey-Sakata Decoding Algorithm.

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