---

＜E-Book＞
Using Algebraic Geometry / by David A. Cox, John Little, Donal O'Shea
(Graduate Texts in Mathematics. ISSN:21975612 ; 185)

Edition	2nd ed. 2005.
Publisher	(New York, NY : Springer New York : Imprint: Springer)
Year	2005
Language	English
Size	XII, 575 p : online resource
Authors	*Cox, David A author Little, John author O'Shea, Donal author SpringerLink (Online service)
Subjects	LCSH:Algebraic geometry LCSH:Computer science -- Mathematics  All Subject Search LCSH:Algorithms FREE:Algebraic Geometry FREE:Symbolic and Algebraic Manipulation FREE:Algorithms
Notes	Solving Polynomial Equations -- Resultants -- Computation in Local Rings -- Modules -- Free Resolutions -- Polytopes, Resultants, and Equations -- Polyhedral Regions and Polynomials -- Algebraic Coding Theory -- The Berlekamp-Massey-Sakata Decoding Algorithm 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 HTTP:URL=https://doi.org/10.1007/b138611

 Similar Items