The Algorithmic Resolution of Diophantine Equations: A Computational Cookbook (London Mathematical Society Student Texts, Series Number 41) - Hardcover

Smart, Nigel P.

Hardcover

ISBN 10: 052164156X ISBN 13: 9780521641562

Publisher: Cambridge University Press, 1999

Synopsis

Beginning with a brief introduction to algorithms and diophantine equations, this volume provides a coherent modern account of the methods used to find all the solutions to certain diophantine equations, particularly those developed for use on a computer. The study is divided into three parts, emphasizing approaches with a wide range of applications. The first section considers basic techniques including local methods, sieving, descent arguments and the LLL algorithm. The second section explores problems that can be solved using Baker's theory of linear forms in logarithms. The final section looks at problems associated with curves, focusing on rational and integral points on elliptic curves. Each chapter concludes with a useful set of exercises. A detailed bibliography is included. This book will appeal to graduate students and research workers interested in solving diophantine equations using computational methods.

About this title

Book Description

A coherent modern account of the computational methods used to solve diophantine equations. The emphasis is on approaches with wide ranging applications. After a brief introduction, the first section considers basic techniques. The second section explores problems which can be solved using Baker's theory of linear forms in logarithms. The final section looks at problems associated with curves. Useful exercises and a detailed bibliography are included.Requiring a basic knowledge of number theory, this book will appeal to graduate students and research workers.

Review

"It is high time for such a book to appear...professional mathematicians and even experts in the subject will find it useful as well...Smart did a good job,and his book will efficiently serve as a textbook for beginners and as a reference source for the experts." Mathematical Reviews

"It is a real pleasure to read this book, mainly because the author gives many examples and many practical remarks concerning the effective solution of diophantine equations. ...this is a very attractive book, full of concrete information, which gives a very clear and lucid view of the current knowledge." Bulletin of the AMS

Edition details

• Publisher: Cambridge University Press
• Publication date: 1999
• Language: English
• ISBN 10: 052164156X
• ISBN 13: 9780521641562
• Binding: Hardcover
• Edition number: 1
• Number of pages: 260