Using algebraic geometry
著者
書誌事項
Using algebraic geometry
（Graduate texts in mathematics, 185）
Springer, c1998
- : hard
- : pbk
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注記
Includes bibliographical references (p. 468-475) and index
内容説明・目次
- 巻冊次
-
: hard ISBN 9780387984872
内容説明
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.
目次
- Solving polynomial equations
- resultants
- computation in local rings
- modules
- free resolutions
- polytopes, resultants and equations
- integer programming, combinatorics and splines
- algebraic coding theory.
- 巻冊次
-
: pbk ISBN 9780387984926
内容説明
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 Gr"obner bases and resultants. In order to do this, the authors provide an introduction to some algebraic objects and techniques which are more advanced than one typically encounters in a first course, but nonetheless of great utility. 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 Gr"obner bases. The book does not assume the reader is familiar with more advanced concepts such as modules.
目次
1: Introduction. 2: Solving Polynomial Equations. 3: Resultants. 4: Computation in Local Rings. 5: Modules. 6: Free Resolutions. 7: Polytopes, Resultants and Equations. 8: Integer Programming, Combinatorics and Splines. 9: Algebraic Coding Theory.
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