Computations in Algebraic Geometry with Macaulay 2

David Eisenbud, Daniel R. Grayson, Michael Stillman, Bernd Sturmfels

330 pages, parution le 01/09/2001

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Résumé

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.

Contents

Preface

Introducing Macaulay 2

Ideals, varieties and Macaulay 2
Projective geometry and homological algebra
Data types, functions, and programmingv
Teaching the geometrfy of schemes

Mathematical computations

Monomial ideas
From enumerative geometry to solving systems of polynomial equations
Resolutions and cohomology over complete intersections
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

L'auteur - Michael Stillman

Michael Still has worked on large-scale image processing and storage for several years, including a couple of years managing and developing large image databases for an Australian government department. Michael has extensive experience developing on Windows platforms, as well as various forms of Unix, including AIX, FreeBSD, and Linux. Michael holds a bachelor's degree in computer engineering from the University of Canberra, and he is currently working toward his PhD in operating systems implementation from the Australian National University.

Still is the author of several articles on ImageMagick for IBM DeveloperWorks, and he has also written articles on TIFF programming with libtiff as well as other imaging topics.

L'auteur - Bernd Sturmfels

Bernd Sturmfels received doctoral degrees in 1987 from the University of Washington, Seattle and TU Darmstadt, Germany. After two postdoc years at the IMA in Minneapolis and RISC-Linz in Austria, he taught at Cornell University before joining UC Berkeley in 1995, where he is now Professor of Mathematics and Computer Science. A leading experimentalist among mathematicians, Sturmfels has authored seven books and over 130 research articles in the areas of combinatorics, algebraic geometry, symbolic computation, and their applications, and he has mentored 16 doctoral students.

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	David Eisenbud, Daniel R. Grayson, Michael Stillman, Bernd Sturmfels
Parution	01/09/2001
Nb. de pages	330
Format	16 x 24
Couverture	Relié
Poids	652g
Intérieur	Noir et Blanc
EAN13	9783540422303