Computations in Algebraic Geometry With Macaulay 2,9783540422303

Computations in Algebraic Geometry With Macaulay 2

by ; ; ;
ISBN13: 9783540422303
ISBN10: 3540422307
Format: Hardcover
Pub. Date: 2002-01-01
Publisher(s): PALGRAVE MACMILLAN
  • Free Shipping Icon

    Free Shipping On Orders Over $35

    Your order must be $35 or more to qualify for free economy shipping. Marketplace items, eBooks and apparel do not qualify towards the $35 purchase minimum.

  • eCampus.com Device Compatibility Matrix

    Click the device icon to install or view instructions

    Apple iOS | iPad, iPhone, iPod
    Apple iOS | iPad, iPhone, iPod
    Android Devices | Android Tables & Phones OS 2.2 or higher | *Kindle Fire
    Android Devices | Android Tables & Phones OS 2.2 or higher | *Kindle Fire
    Windows 10 / 8 / 7 / Vista / XP
    Windows 10 / 8 / 7 / Vista / XP
    Mac OS X | **iMac / Macbook
    Mac OS X | **iMac / Macbook
    Enjoy offline reading with these devices
    Apple Devices
    Android Devices
    Windows Devices
    Mac Devices
    iPad, iPhone, iPod
    Our reader is compatible
     
     
     
    Android 2.2 +
     
    Our reader is compatible
     
     
    Kindle Fire
     
    Our reader is compatible
     
     
    Windows
    10 / 8 / 7 / Vista / XP
     
     
    Our reader is compatible
     
    Mac
     
     
     
    Our reader is compatible
List Price: $106.65

Buy New

Usually Ships in 8 - 10 Business Days.
$106.54
Add to Cart

Rent Textbook

Select for Price
Add to Cart
There was a problem. Please try again later.

Rent Digital

Rent Digital Options
Online:30 Days access
Downloadable:30 Days
$19.80
Online:60 Days access
Downloadable:60 Days
$26.40
Online:90 Days access
Downloadable:90 Days
$33.00
Online:120 Days access
Downloadable:120 Days
$39.60
Online:180 Days access
Downloadable:180 Days
$42.90
Online:1825 Days access
Downloadable:Lifetime Access
$65.99
$42.90
Add to Cart

Used Textbook

We're Sorry
Sold Out

Buy from our Marketplace starting at $52.12

How Marketplace Works:

  • This item is offered by an independent seller and not shipped from our warehouse
  • Item details like edition and cover design may differ from our description; see seller's comments before ordering.
  • Sellers much confirm and ship within two business days; otherwise, the order will be cancelled and refunded.
  • Marketplace purchases cannot be returned to eCampus.com. Contact the seller directly for inquiries; if no response within two days, contact customer service.
  • Additional shipping costs apply to Marketplace purchases. Review shipping costs at checkout.

Summary

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.

Table of Contents

Preface v
List of Contributors
xv
Part I Introducing Macaulay 2(323)
Ideals, Varieties and Macaulay 2
3(14)
Bernd Sturmfels
A Curve in Affine Three-Space
3(1)
Intersecting Our Curve With a Surface
4(2)
Changing the Ambient Polynomial Ring
6(2)
Monomials Under the Staircase
8(4)
Pennies, Nickels, Dimes and Quarters
12(5)
References
15(2)
Projective Geometry and Homological Algebra
17(24)
David Eisenbud
The Twisted Cubic
18(2)
The Cotangent Bundle of P3
20(4)
The Cotangent Bundle of a Projective Variety
24(2)
Intersections by Serre's Method
26(2)
A Mystery Variety in P3
28(13)
Appendix A. How the ``Mystery Variety'' was Made
37(3)
References
40(1)
Data Types, Functions, and Programming
41(14)
Daniel R. Grayson
Michael E. Stillman
Basic Data Types
41(3)
Control Structures
44(2)
Input and Output
46(2)
Hash Tables
48(4)
Methods
52(1)
Pointers to the Source Code
53(2)
References
53(2)
Teaching the Geometry of Schemes
55(18)
Gregory G. Smith
Bernd Sturmfels
Distinguished Open Sets
55(1)
Irreducibility
56(2)
Singular Points
58(2)
Fields of Definition
60(1)
Multiplicity
61(1)
Flat Families
62(1)
Bezout's Theorem
63(1)
Constructing Blow-ups
64(1)
A Classic Blow-up
65(3)
Fano Schemes
68(5)
References
70(3)
Part II Mathematical Computations
Monomial Ideals
73(28)
Serkan Hosten
Gregory G. Smith
The Basics of Monomial Ideals
74(3)
Primary Decomposition
77(6)
Standard Pairs
83(6)
Generic Initial Ideals
89(6)
The Chain Property
95(6)
References
99(2)
From Enumerative Geometry to Solving Systems of Polynomial Equations
101(30)
Frank Sottile
Introduction
101(2)
Solving Systems of Polynomials
103(9)
Some Enumerative Geometry
112(2)
Schubert Calculus
114(7)
The 12 Lines: Reprise
121(10)
References
128(3)
Resolutions and Cohomology over Complete Intersections
131(48)
Luchezar L. Avramov
Daniel R. Grayson
Matrix Factorizations
133(6)
Graded Algebras
139(2)
Universal Homotopies
141(4)
Cohomology Operators
145(5)
Computation of Ext Modules
150(7)
Invariants of Modules
157(13)
Invariants of Pairs of Modules
170(9)
Appendix A. Gradings
176(1)
References
177(2)
Algorithms for the Toric Hilbert Scheme
179(36)
Michael Stillman
Bernd Sturmfels
Rekha Thomas
Generating Monomial Ideals
182(6)
Polyhedral Geometry
188(5)
Local Equations
193(6)
The Coherent Component of the Toric Hilbert Scheme
199(16)
Fourier-Motzkin Elimination
206(5)
Minimal Presentation of Rings
211(2)
References
213(2)
Sheaf Algorithms Using the Exterior Algebra
215(36)
Wolfram Decker
David Eisenbud
Introduction
215(3)
Basics of the Bernstein-Gel'fand-Gel'fand Correspondence
218(4)
The Cohomology and the Tate Resolution of a Sheaf
222(4)
Cohomology and Vector Bundles
226(4)
Cohomology and Monads
230(6)
The Beilinson Monad
236(5)
Examples
241(10)
References
247(4)
Needles in a Haystack: Special Varieties via Small Fields
251(30)
Frank-Olaf Schreyer
Fabio Tonoli
How to Make Random Curves up to Genus 14
253(10)
Comparing Green's Conjecture for Curves and Points
263(4)
Pfaffian Calabi-Yau Threefolds in P6
267(14)
References
277(4)
D-modules and Cohomology of Varieties
281(44)
Uli Walther
Introduction
282(3)
The Weyl Algebra and Grobner Bases
285(7)
Bernstein-Sato Polynomials and Localization
292(12)
Local Cohomology Computations
304(9)
Implementation, Examples, Questions
313(12)
References
321(4)
Index 325

An electronic version of this book is available through VitalSource.

This book is viewable on PC, Mac, iPhone, iPad, iPod Touch, and most smartphones.

By purchasing, you will be able to view this book online, as well as download it, for the chosen number of days.

Digital License

You are licensing a digital product for a set duration. Durations are set forth in the product description, with "Lifetime" typically meaning five (5) years of online access and permanent download to a supported device. All licenses are non-transferable.

More details can be found here.

A downloadable version of this book is available through the eCampus Reader or compatible Adobe readers.

Applications are available on iOS, Android, PC, Mac, and Windows Mobile platforms.

Please view the compatibility matrix prior to purchase.