Computations in Algebraic Geometry with Macaulay 2

Computations in Algebraic Geometry with Macaulay 2
Author: David Eisenbud
Publisher: Springer Science & Business Media
Total Pages: 354
Release: 2001-09-25
Genre: Mathematics
ISBN: 9783540422303

This book presents algorithmic tools for algebraic geometry, with experimental applications. It also introduces Macaulay 2, a computer algebra system supporting research in algebraic geometry, commutative algebra, and their applications. The algorithmic tools presented here are designed to serve readers wishing to bring such tools to bear on their own problems. The first part of the book covers Macaulay 2 using concrete applications; the second emphasizes details of the mathematics.

Computations in Algebraic Geometry with Macaulay 2

Computations in Algebraic Geometry with Macaulay 2
Author: David Eisenbud
Publisher: Springer Science & Business Media
Total Pages: 335
Release: 2013-03-14
Genre: Mathematics
ISBN: 3662048515

This book presents algorithmic tools for algebraic geometry, with experimental applications. It also introduces Macaulay 2, a computer algebra system supporting research in algebraic geometry, commutative algebra, and their applications. The algorithmic tools presented here are designed to serve readers wishing to bring such tools to bear on their own problems. The first part of the book covers Macaulay 2 using concrete applications; the second emphasizes details of the mathematics.

Computing in Algebraic Geometry

Computing in Algebraic Geometry
Author: Wolfram Decker
Publisher: Springer Science & Business Media
Total Pages: 331
Release: 2006-03-02
Genre: Mathematics
ISBN: 3540289925

This book provides a quick access to computational tools for algebraic geometry, the mathematical discipline which handles solution sets of polynomial equations. Originating from a number of intense one week schools taught by the authors, the text is designed so as to provide a step by step introduction which enables the reader to get started with his own computational experiments right away. The authors present the basic concepts and ideas in a compact way.

Computational Algebraic Geometry

Computational Algebraic Geometry
Author: Hal Schenck
Publisher: Cambridge University Press
Total Pages: 212
Release: 2003-10-06
Genre: Computers
ISBN: 9780521536509

The interplay between algebra and geometry is a beautiful (and fun!) area of mathematical investigation. Advances in computing and algorithms make it possible to tackle many classical problems in a down-to-earth and concrete fashion. This opens wonderful new vistas and allows us to pose, study and solve problems that were previously out of reach. Suitable for graduate students, the objective of this 2003 book is to bring advanced algebra to life with lots of examples. The first chapters provide an introduction to commutative algebra and connections to geometry. The rest of the book focuses on three active areas of contemporary algebra: Homological Algebra (the snake lemma, long exact sequence inhomology, functors and derived functors (Tor and Ext), and double complexes); Algebraic Combinatorics and Algebraic Topology (simplicial complexes and simplicial homology, Stanley-Reisner rings, upper bound theorem and polytopes); and Algebraic Geometry (points and curves in projective space, Riemann-Roch, Cech cohomology, regularity).

A First Course in Computational Algebraic Geometry

A First Course in Computational Algebraic Geometry
Author: Wolfram Decker
Publisher: Cambridge University Press
Total Pages: 127
Release: 2013-02-07
Genre: Computers
ISBN: 1107612535

A quick guide to computing in algebraic geometry with many explicit computational examples introducing the computer algebra system Singular.

The Geometry of Schemes

The Geometry of Schemes
Author: David Eisenbud
Publisher: Springer Science & Business Media
Total Pages: 265
Release: 2006-04-06
Genre: Mathematics
ISBN: 0387226397

Grothendieck’s beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.

Computational Commutative Algebra 1

Computational Commutative Algebra 1
Author: Martin Kreuzer
Publisher: Springer Science & Business Media
Total Pages: 325
Release: 2008-07-15
Genre: Mathematics
ISBN: 354067733X

This introduction to polynomial rings, Gröbner bases and applications bridges the gap in the literature between theory and actual computation. It details numerous applications, covering fields as disparate as algebraic geometry and financial markets. To aid in a full understanding of these applications, more than 40 tutorials illustrate how the theory can be used. The book also includes many exercises, both theoretical and practical.

Commutative Algebra

Commutative Algebra
Author: David Eisenbud
Publisher: Springer Science & Business Media
Total Pages: 784
Release: 2013-12-01
Genre: Mathematics
ISBN: 1461253500

This is a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. The book gives a concise treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Many exercises included.

Classical Algebraic Geometry

Classical Algebraic Geometry
Author: Igor V. Dolgachev
Publisher: Cambridge University Press
Total Pages: 653
Release: 2012-08-16
Genre: Mathematics
ISBN: 1139560786

Algebraic geometry has benefited enormously from the powerful general machinery developed in the latter half of the twentieth century. The cost has been that much of the research of previous generations is in a language unintelligible to modern workers, in particular, the rich legacy of classical algebraic geometry, such as plane algebraic curves of low degree, special algebraic surfaces, theta functions, Cremona transformations, the theory of apolarity and the geometry of lines in projective spaces. The author's contemporary approach makes this legacy accessible to modern algebraic geometers and to others who are interested in applying classical results. The vast bibliography of over 600 references is complemented by an array of exercises that extend or exemplify results given in the book.