عنوان

Computations in Algebraic Geometry with Macaulay 2

(Number (ISBN

9783642075926

(Number (ISBN

9783662048511

Number

b406998

Title Proper

Computations in Algebraic Geometry with Macaulay 2

General Material Designation

[Book]

First Statement of Responsibility

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

Place of Publication, Distribution, etc.

Berlin, Heidelberg :

Name of Publisher, Distributor, etc.

Imprint: Springer,

Date of Publication, Distribution, etc.

2002.

Series Title

Algorithms and Computation in Mathematics,

Volume Designation

8

ISSN of Series

1431-1550 ;

Text of Note

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.

0

Text of Note

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.

International Standard Book Number

9783642075926

Title

Springer eBooks

Algebra-- Data processing.

Combinatorics.

Geometry, Algebraic.

Mathematics.

Eisenbud, David.

Grayson, Daniel R.

Stillman, Michael.

Sturmfels, Bernd.

SpringerLink (Online service)

Date of Transaction

20190301075900.0

Electronic name

[Book]

Y