代数几何应用（第二版 英文版）
出版时间：2013年版
内容简介
《代数几何应用（第2版）》中介绍了代数几何的诸多应用，重点强调grabner基和结式的新进展。这是第二版新版本中做了较大改动：单独增加了一部分讨论矩阵如何被运用于特定的单项式序；修订了mora规范形式算术的表示；两节专门讨论了理想的grobner扇和grobner游动基算术；新增一章讲述序域、相关编码和berlekamp-massey-sakata解码算术；更新了参考资料，改进了证明，纠正了排版上的错误。本书由考克斯著。
目录
Preface to the Second EditionPreface to the First EditionIntroduction1 Polynomials and Ideals 2 Monomial Orders and Polynomial Division 3 Gr6bner Bases 4 Affine Varieties2 Solving Polynomial Equations 1 Solving Polynomial Systems by Elimination 2 Finite-Dimensional Algebras 3 Gr6bner Basis Conversion 4 Solving Equations via Eigenvalues and Eigenvectors 5 Real Root Location and Isolation3 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 and Eigenvectors4 Computation in Local Rings 1 Local Rings 2 Multiplicities and Miinor Numbers 3 Term Orders and Division in Local Rings 4 Standard Bases in Local Rings 5 Applications of Standard Bases5 Modules 1 Modules over Rings 2 Monomial Orders and Gr6bner Bases for Modules 3 Computing Syzygies 4 Modules over Local Rings6 Free Resolutions I Presentations and Resolutions of Modules 2 Hilbert's Syzygy Theorem 3 Graded Resolutions 4 Hilbert Polynomials and GeometricApplications 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 Equations8 Polyhedral Regions and Polynomials 1 Integer Programming 2 Integer Programming and Combinatorics 3 Multivariate Polynomial Splines 4 The Gr6bner Fan of an Ideal 5 The Gr6bner Walk9 Algebraic Coding Theory 1 Finite Fields 2 Error-Correcting Codes 3 Cyclic Codes 4 Reed-Solomon Decoding Algorithms10 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 AlgorithmReferencesIndex
