Using Algebraic Geometry - Brossura

Cox, David A.; Little, John; O'Shea, Donal

Brossura

ISBN 10: 0387500960 ISBN 13: 9780387500966

Casa editrice: Springer, 2008

Riassunto

In recent years, the discovery of new algorithms for dealing with polynomial equations, coupled with their implementation on inexpensive yet fast computers, has sparked a minor revolution in the study and practice of algebraic geometry. One of the aims of this text is to illustrate the various uses of algebraic geometry and to highlight the more recent applications of Groebner bases and resultants. In order to do this, an introduction to some advanced algebraic objects and techniques is provided.

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Review:

From the reviews of the second edition:

"The book has been very successful. It succeeded in establishing a bridge between modern computer science and classical algebraic geometry." (Gerhard Pfister, Zentralblatt MATH, Vol. 1079, 2006)

"The authors a ] do not expect much from their reader in terms of mathematical prerequisites. a ] This reviewer thinks that the part of the intended audience consisting of graduate students interested in research in computational algebraic geometry will find this to be a very useful book. The many exercises throughout the text, and the mere fact that this is a very good and detailed overview of the subject will definitely make it desirable for this group." (Gizem Karaali, MathDL, September, 2005)

From the Back Cover:

In recent years, the discovery of new algorithms for dealing with polynomial equations, coupled with their implementation on fast inexpensive computers, has sparked a minor revolution in the study and practice of algebraic geometry. These algorithmic methods have also given rise to some exciting new applications of algebraic geometry. This book illustrates the many uses of algebraic geometry, highlighting some of the more recent applications of Gröbner bases and resultants.

The book is written for nonspecialists and for readers with a diverse range of backgrounds. It assumes knowledge of the material covered in a standard undergraduate course in abstract algebra, and it would help to have some previous exposure to Gröbner bases. The book does not assume the reader is familiar with more advanced concepts such as modules.

For the new edition, the authors have added a unified discussion of how matrices can be used to specify monomial orders; a revised presentation of the Mora normal form algorithm; two sections discussing the Gröbner fan of an ideal and the Gröbner Walk basis conversion algorithm; and a new chapter on the theory of order domains, associated codes, and the Berlekamp-Massey-Sakata decoding algorithm. They have also updated the references, improved some of the proofs, and corrected typographical errors.

David Cox is Professor of Mathematics at Amherst College. John Little is Professor of Mathematics at College of the Holy Cross. Dona

l O’Shea is the Elizabeth T. Kennan Professor of Mathematics and Dean of Faculty at Mt. Holyoke College. These authors also co-wrote the immensely successful book, Ideals, Varieties, and Algorithms.

Su questa edizione

• Editore: Springer
• Data di pubblicazione: 2008
• ISBN 10: 0387500960
• ISBN 13: 9780387500966
• Rilegatura: Paperback
• Numero di pagine: 588