Computations in Algebraic Geometry with Macaulay 2
By: edited by David Eisenbud, Michael Stillman, Daniel R. Grayson, Bernd Sturmfels
Contributors: Stillman, Michael; Grayson, Daniel R.; Sturmfels, Bernd
Series: Algorithms and Computation in Mathematics -- 8; Algorithms and Computation in Mathematics -- 8
Publisher: Springer Berlin Heidelberg
Published: 2002
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] /
Number of pages: 329
ISBN-13: 9783642075926; 9783662048511
Subjects: Combinatorics; Mathematics; Algebra; Data processing; Geometry, algebraic
Description: 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.
Notes: Online full text is restricted to subscribers.

Also available in print.

Mode of access: World Wide Web.
Table of contents: title: Part I. Introducing Macaulay 2: 1. Ideals, Varieties and Macaulay 2 by Bernd Sturmfels; title: 2. Projective Geometry and Homological Algebra by David Eisenbud; title: 3. Data Types, Functions, and Programming by Daniel R. Grayson and Michael E. Stillman; title: 4. Teaching the Geometry of Schemes by Gregory G. Smith and Bernd Sturmfels; title: Part II. Mathematical Computations: 5. Monomial Ideals by Serkan Hosten and Gregory G. Smith; title: 6. From Enumerative Geometry to Solving Systems of Polynomial Equations by Frank Sottile; title: 7. Resolutions and Cohomology over Complete Intersections by Luchezar L. Avramov and Daniel R. Grayson; title: 8. Algorithms for the Toric Hilbert Scheme by Stillman, Bernd Sturmfels, and Rekha Thomas; title: 9. Sheaf Algorithms Using the Exterior Algebra by Wolfram Decker and David Eisenbud; title: 10. Needles in a Haystack: Special Varieties via Small Fields by Frank-Olaf Schreyer and Fabio Tonoli; title: 11.D-modules and Cohomology of Varieties by Uli Walther.