代数几何应用（第二版 英文版）

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