The Algorithmic Resolution of Diophantine Equations

Nigel P. Smart

ISBN 10: 0521646332 / ISBN 13: 9780521646338

Published by Cambridge University Press, 1999

About this Item

Druck auf Anfrage Neuware - Printed after ordering - 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.

Seller Inventory # 9780521646338

Bibliographic Details

• Title: The Algorithmic Resolution of Diophantine Equations
• Publisher: Cambridge University Press
• Publication Date: 1999
• Language: English
• ISBN 10: 0521646332
• ISBN 13: 9780521646338
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 229W x 152H x 15D millimeters 229 millimeters width by 152 millimeters height by 15 millimeters depth
• Weight: 427 grams

About this title

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.

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.