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介紹了代數幾何的諸多應用，重點強調grabner基和結式的新進展。這是第二版新版本中做了較大改動：單獨增加了一部分討論矩陣如何被運用於特定的單項式序；修訂了mora規范形式算術的表示；兩節專門討論了理想的grobner扇和grobner游動基算術；新增一章講述序域、相關編碼和berlekamp—massey—sakata解碼算術；更新了參考資料，改進了證明，糾正了排版上的錯誤。
Preface to the Second Edition
Preface to the First Edition
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 and Eigenvectors
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 and Eigenvectors
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
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
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
Polyhedral Regions and Polynomials
1 Integer Programming
2 Integer Programming and Combinatorics
3 Multivariate Polynomial Splines
4 The Grobner Fan of an Ideal
5 The Grobner Walk
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
