Computational Commutative and Non-commutative Algebraic Geometry PDF Download

Author: Svetlana Cojocaru
Publisher: IOS Press
ISBN: 1586035053
Category : Electronic books
Languages : en
Pages : 336

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Book Description

Author: Martin Kreuzer
Publisher: Springer Science & Business Media
ISBN: 3540706283
Category : Mathematics
Languages : en
Pages : 326

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Book Description
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.

Author: David Eisenbud
Publisher: Cambridge University Press
ISBN: 1107065623
Category : Mathematics
Languages : en
Pages : 463

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Book Description
This book surveys fundamental current topics in these two areas of research, emphasising the lively interaction between them. Volume 1 contains expository papers ideal for those entering the field.

Author: Wolmer Vasconcelos
Publisher: Springer Science & Business Media
ISBN: 9783540213116
Category : Mathematics
Languages : en
Pages : 432

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Book Description
This ACM volume deals with tackling problems that can be represented by data structures which are essentially matrices with polynomial entries, mediated by the disciplines of commutative algebra and algebraic geometry. The discoveries stem from an interdisciplinary branch of research which has been growing steadily over the past decade. The author covers a wide range, from showing how to obtain deep heuristics in a computation of a ring, a module or a morphism, to developing means of solving nonlinear systems of equations - highlighting the use of advanced techniques to bring down the cost of computation. Although intended for advanced students and researchers with interests both in algebra and computation, many parts may be read by anyone with a basic abstract algebra course.

Author: F.M.J. van Oystaeyen
Publisher: Springer
ISBN: 3540386017
Category : Mathematics
Languages : en
Pages : 408

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Book Description

Author: David Eisenbud
Publisher: Cambridge University Press
ISBN: 110714972X
Category : Mathematics
Languages : en
Pages : 303

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Book Description
This book surveys fundamental current topics in these two areas of research, emphasising the lively interaction between them. Volume 2 focuses on the most recent research.

Author: Y. Manin
Publisher: Princeton University Press
ISBN: 1400862515
Category : Mathematics
Languages : en
Pages : 173

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Book Description
There is a well-known correspondence between the objects of algebra and geometry: a space gives rise to a function algebra; a vector bundle over the space corresponds to a projective module over this algebra; cohomology can be read off the de Rham complex; and so on. In this book Yuri Manin addresses a variety of instances in which the application of commutative algebra cannot be used to describe geometric objects, emphasizing the recent upsurge of activity in studying noncommutative rings as if they were function rings on "noncommutative spaces." Manin begins by summarizing and giving examples of some of the ideas that led to the new concepts of noncommutative geometry, such as Connes' noncommutative de Rham complex, supergeometry, and quantum groups. He then discusses supersymmetric algebraic curves that arose in connection with superstring theory; examines superhomogeneous spaces, their Schubert cells, and superanalogues of Weyl groups; and provides an introduction to quantum groups. This book is intended for mathematicians and physicists with some background in Lie groups and complex geometry. Originally published in 1991. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Author: Gwyn Bellamy
Publisher: Cambridge University Press
ISBN: 1107129540
Category : Mathematics
Languages : en
Pages : 367

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Book Description
This book provides a comprehensive introduction to the interactions between noncommutative algebra and classical algebraic geometry.

Author: Martin Kreuzer
Publisher: Springer
ISBN: 9783540677338
Category : Mathematics
Languages : en
Pages : 322

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Book Description
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.

Author: Gert-Martin Greuel
Publisher: Springer Science & Business Media
ISBN: 3662049635
Category : Mathematics
Languages : en
Pages : 601

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Book Description
This book can be understood as a model for teaching commutative algebra, and takes into account modern developments such as algorithmic and computational aspects. As soon as a new concept is introduced, the authors show how the concept can be worked on using a computer. The computations are exemplified with the computer algebra system Singular, developed by the authors. Singular is a special system for polynomial computation with many features for global as well as for local commutative algebra and algebraic geometry. The book includes a CD containing Singular as well as the examples and procedures explained in the book.