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　　分類: 图书,进口原版书,科学与技术 Science & Techology ,

作者： David Eisenbud，Daniel R. Grayson等著

出 版 社： 湖南文艺出版社

出版时间： 2001-10-1字数：版次：页数： 329印刷时间： 2001/10/01开本： 16开印次：纸张： 胶版纸I S B N ： 9783540422303包装： 精装内容简介

This book presents algorithmic tools for algebraic geometry and experimental applications of them. It also introduces a software system in which the tools have been implemented and with which the experiments can be carried out. Macaulay 2 is a computer algebra system devoted to supporting research in algebraic geometry, commutative algebra, and their applications. The reader of this book will encounter Macaulay 2 in the context of concrete applications and practical computations in algebraic geometry. The expositions of the algorithmic tools presented here are designed to serve as a useful guide for those wishing to bring such tools to bear on their own problems. These expositions will be valuable to both the users of other programs similar to Macaulay 2 (for example, Singular and CoCoA) and those who are not interested in explicit machine computations at all. The first part of the book is primarily concerned with introducing Macaulay2, whereas the second part emphasizes the mathematics.

目录

Preface

List of Contributors

Part I Introducing Macaulay 2

Ideals, Varieties and Macaulay 2

Bernd Sturmfels

1A Curve in Affine Three-Space

2Intersecting Our Curve With a Surface

3Changing the Ambient Polynomial Ring

4Monomials Under the Staircase

5Pennies, Nickels, Dimes and Quarters

References

Projective Geometry and Homological Algebra

David Eisenbud

1The Twisted Cubic

2The Cotangent Bundle of I?3

3The Cotangent Bundle of a Projective Variety

4Intersections by Serre's Method

5A Mystery Variety in ]?3

Appendix A. How the "Mystery Variety" was Made

References

Data Types, Fhlnctions, and Programming

Daniel R. Grayson and Michael E. Stillman

1Basic Data Types

2Control Structures

3Input and Output

4Hash Tables

5Methods

6Pointers to the Source Code

References

Teaching the Geometry of Schemes

Gregory G. Smith and Bernd Sturmfels

1Distinguished Open Sets

2Irreducibility

3Singular Point

4Fields of Definition

5Multiplicity

6Flat Families

7Bezout's Theorem

8Constructing Blow-ups

9A Classic Blow-up

10 Fano Schemes

References

Part II Mathematical Computations

Monomial Ideals

Serkan Hosaten and Gregory G. Smith

1The Basics of Monomial Ideals

2Primary Decomposition

3Standard Pairs

4Generic Initial Ideals

5The Chain Property

References

From Enumerative Geometry to Solving Systems of Polynomial Equations

Frank Sottile

1Introduction

2Solving Systems of Polynomials

3Some Enumerative Geometry

4Schubert Calculus

5The 12 Lines: Reprise

References

Resolutions and Cohomology over Complete Intersections

Luchezar L. Avramov and Daniel R. Grayson

1Matrix Factorizations

2Graded Algebras

3UniversM Homotopies

4Cohomology Operators

5Computation of Ext Modules

6Invariants of Modules

7Invariants of Pairs of Modules

Appendix A. Gradings

References

Algorithms for the Toric Hilbert Scheme

Sheaf Algorithms Using the Exterior Algebra

Needles in a Haystack:Special Varieties via Small Fields

D-modules and Cohomology of Varieties

Index

 

 

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