Table of Contents

Table of Contents of
An Introduction to Grobner Bases
W.W. Adams and P. Loustaunau
Graduate Studies in Mathematics, Vol. 3
American Mathematical Society, 289 p., 1994.

Order Information

Preface

Chapter 1. Basic Theory of Grobner Bases

1.1 Introduction

1.2 The Linear Case

1.3 The One Variable Case

1.4 Term Orders

1.5 Division Algorithm

1.6 Grobner Bases

1.7 S-Polynomials and Buchberger's Algorthm

1.8 Reduced Grobner Bases

1.9 Summary

Chapter 2. Applications of Grobner Bases

2.1 Elementary Applications of Grobner Bases

2.2 Hilbert Nullstellensatz

2.3 Elimination

2.4 Polynomial Maps

2.5 Some Applications to Algebraic Geometry

2.6 Minimal Polynomials of Elements in Field Extension

2.7 The 3-Color Problem

2.8 Integer Programming

Chapter 3. Modules and Grobner Bases

3.1 Modules

3.2 Grobner Bases and Syzygies

3.3 Improvements on Buchberger's Algorithm

3.4 Computation of the Syzygy Module

3.5 Grobner Bases for Modules

3.6 Elementary Applications of Grobner Bases for Modules

3.7 Syzygies for Modules

3.8 Applications of Syzygies

3.9 Computation of Hom

3.10 Free Resolutions

Chapter 4. Grobner Bases over Rings

4.1 Basic Defnitions

4.2 Computing Grobner Bases over Rings

4.3 Applications of Grobner Bases over Rings

4.4 A Primality Test

4.5 Grobner Bases over Principal Ideal Domain

4.6 Primary Decomposition in R[x] for R a PID

Appendix A. Computations and Algorithms

Appendix B. Well-Ordering and Induction

References

List of Symbols

Index