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

Smart, Nigel P.

Softcover

ISBN 10: 0521646332 ISBN 13: 9780521646338

Publisher: Cambridge University Press, 1998

Synopsis

Beginning with a brief introduction to algorithms and diophantine equations, this volume aims to provide a coherent account of the methods used to find all the solutions to certain diophantine equations, particularly those procedures which have been developed for use on a computer. The study is divided into three parts, the emphasis throughout being on examining 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 which can be solved using Baker's theory of linear forms in logarithms. The final section looks at problems associated with curves, mainly 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, with a basic knowledge of number theory, who are interested in solving diophantine equations using computational methods.

About this title

Review

'... should certainly establish itself as a key reference for established researchers and a natural starting point for new PhD students in the area.' E. V. Flynn, Bulletin of the London Mathematical Society

Book Description

A coherent account of the computational methods used to solve diophantine equations. Topics include local methods, sieving, descent arguments, the LLL algorithm, Baker's theory of linear forms in logarithms, and problems associated with curves. Useful exercises and bibliography are included. Suitable for graduate students and research workers.

Edition details

• Publisher: Cambridge University Press
• Publication date: 1998
• Language: English
• ISBN 10: 0521646332
• ISBN 13: 9780521646338
• Binding: Paperback
• Number of pages: 260