Using algebraic geometry使用代数的几何学
点此进入淘宝搜索页搜索分類: 图书,进口原版书,科学与技术 Science & Techology ,
作者： David A. Cox等著
出 版 社：
出版时间： 2005-3-1字数：版次： 1页数： 572印刷时间： 2005/03/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9780387207339包装： 平装内容简介
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.
目录
Preface to the Second Edidtion
Preface to the First Edition
1 Introduction
1 Polynomials and Ideals
2 Monomial Orders and Polynomial Division
3 Grobner Bases
4 Affine Varieties
2 Solving Polynomial Equations
1 Solving Polynomial Systems by Elimination
2 Finite-Dimensional Algebras
3 Grobner Basis Conversion
4 Solving Equations via Eigenvalues
5 Real Root Location and Isolation
3. Resultants
1 The Resultant of Two Polynomials
2 Multipolynomial Resultants
3 Properties of Resultants
4 Computing Resultants
5 Solving Equations via Resultants
6 Solving Equations via Eigenvalues
4. Computation in Local Rings
1 Local Rings
2 Multiplicities and Milnor Numbers
3 Term Orders and Division in Local Rings
4 Standard Bases in Local Rings
5 Applications of Standard Bases
5. Modules
1 Modules over Rings
2 Monomial Orders and Grobner Bases for Modules
3 Computing Syzygies
4 Modules over Local Rings
6. Free Resolutions
1 Presentations and Resolutions of Modules
2 Hilbert's Syzygy Theorem
3 Graded Resolutions
4 Hilbert Polynomials and Geometric Applications
7. Polytopes, Resultants and Equations
1 Geometry of Polytopes
2 Sparse Resultants
3 Toric Varieties
4 Minkowski Sums and Mixed Volumes
5 Bernstein's Theorem
6 Computing Resultants and Solving Equations
9 Algebraic Coding Theory
1 Finite Fields
2 Error-Correcting Codes
3 Cyclic Codes
4 Reed-Solomon Decoding Algorithms
10 The Berlekamp-Massey-Sakata Decoding Algorithm
1 Codes from Order Domains
2 The Overall Structure of the BMS Algorithm
3 The Details of the BMS Algorithm
References
Index
