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Using Algebraic Geometry

  • Textbook
  • © 2005

Overview

Authors:
  1. David A. Cox

    1. Department of Mathematics, Amherst College, Amherst, USA

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    You can also search for this author in PubMed   Google Scholar

  2. John Little

    1. Department of Mathematics, College of the Holy Cross, Worcester, USA

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    You can also search for this author in PubMed   Google Scholar

  3. Donal O’shea

    1. Department of Mathematics, Mount Holyoke College, South Hadley, USA

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Graduate Texts in Mathematics (GTM, volume 185)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xii
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  2. Introduction

    Pages 1-25

  3. Solving Polynomial Equations

    Pages 26-76

  4. Resultants

    Pages 77-136

  5. Computation in Local Rings

    Pages 137-188

  6. Modules

    Pages 189-246

  7. Free Resolutions

    Pages 247-304

  8. Polytopes, Resultants, and Equations

    Pages 305-375

  9. Polyhedral Regions and Polynomials

    Pages 376-450

  10. Algebraic Coding Theory

    Pages 451-493

  11. The Berlekamp-Massey-Sakata Decoding Algorithm

    Pages 494-532

  12. Back Matter

    Pages 533-572
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About this book

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. In order to do this, the authors provide an introduction to some algebraic objects and techniques which are more advanced than one typically encounters in a first course, but nonetheless of great utility. 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 this new edition the authors added two new sections and a new chapter, updated the references and made numerous minor improvements throughout the text.

Authors and Affiliations

  • Department of Mathematics, Amherst College, Amherst, USA

    David A. Cox

  • Department of Mathematics, College of the Holy Cross, Worcester, USA

    John Little

  • Department of Mathematics, Mount Holyoke College, South Hadley, USA

    Donal O’shea

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