Using Algebraic Geometry
(Sprache: Englisch)
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...
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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. TOC: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.
Klappentext zu „Using Algebraic Geometry “
The discovery of new algorithms for dealing with polynomial equations, and their implementation on fast, inexpensive computers, has revolutionized algebraic geometry and led to exciting new applications in the field. This book details many uses of algebraic geometry and highlights recent applications of Grobner bases and resultants. This edition contains two new sections, a new chapter, updated references and many minor improvements throughout.
Inhaltsverzeichnis zu „Using Algebraic Geometry “
- 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
Autoren-Porträt von David A. Cox, John B. Little, Donal B. O'Shea
Donal O Shea, geboren 1952, ist Professor für Mathematik am Mount Holyoke College in Massachusetts. Für seine mathematischen Arbeiten zur Theorie der Singularitäten ist er international bekannt geworden. Er hat zahlreiche Forschungsbeiträge veröffentlicht und übersetzt aus dem Russischen und Französischen.
Bibliographische Angaben
- Autoren: David A. Cox , John B. Little , Donal B. O'Shea
- 2005, 2nd ed., 575 Seiten, Maße: 15,3 x 24,1 cm, Kartoniert (TB), Englisch
- Verlag: Springer, New York
- ISBN-10: 0387207333
- ISBN-13: 9780387207339
Sprache:
Englisch
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