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＜電子ブック＞
Computations in Algebraic Geometry with Macaulay 2 / edited by David Eisenbud, Daniel R. Grayson, Mike Stillman, Bernd Sturmfels
(Algorithms and Computation in Mathematics ; 8)

版	1st ed. 2002.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2002
本文言語	英語
大きさ	XV, 329 p. 1 illus : online resource
著者標目	Eisenbud, David editor Grayson, Daniel R editor Stillman, Mike editor Sturmfels, Bernd editor SpringerLink (Online service)
件　名	LCSH:Algebraic geometry LCSH:Computer software LCSH:Discrete mathematics LCSH:Computer science -- Mathematics  全ての件名で検索 FREE:Algebraic Geometry FREE:Mathematical Software FREE:Discrete Mathematics FREE:Symbolic and Algebraic Manipulation
一般注記	I Introducing Macaulay 2 -- Ideals, Varieties and Macaulay 2 -- Projective Geometry and Homological Algebra -- Data Types, Functions, and Programming -- Teaching the Geometry of Schemes -- II Mathematical Computations -- Monomial Ideals -- 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 Systems of polynomial equations arise throughout mathematics, science, and engineering. Algebraic geometry provides powerful theoretical techniques for studying the qualitative and quantitative features of their solution sets. Re­ cently developed algorithms have made theoretical aspects of the subject accessible to a broad range of mathematicians and scientists. The algorith­ mic approach to the subject has two principal aims: developing new tools for research within mathematics, and providing new tools for modeling and solv­ ing problems that arise in the sciences and engineering. A healthy synergy emerges, as new theorems yield new algorithms and emerging applications lead to new theoretical questions. This book presents algorithmic tools for algebraic geometry and experi­ mental 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. A wide range of mathematical scientists should find these expositions valuable. This includes 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 HTTP:URL=https://doi.org/10.1007/978-3-662-04851-1

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