The algorithmic resolution of diophantine equations / Nigel P. Smart

Por: Smart, Nigel PTipo de material: TextoTextoSeries London mathematical society student texts ; 41Detalles de publicación: Cambridge : Cambridge University Press, 1998 Descripción: XVI, 243 p. ; 23 cmISBN: 0-521-64633-2Tema(s): Ecuaciones diferencialesResumen: Beginning with a brief introduction to algorithms and diophantine equations, this volume aims to provide a coherent modern 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.Resumen: Índice: Preface; 1. Introduction; Part I. BASIC SOLUTION TECHNIQUES: 2. Local methods; 3. Applications of local methods to diophantine equations; 4. Ternary quadratic forms; 5. Computational diophantine approximation; 6. Applications of the LLL-algorithm; Part II. METHODS USING LINEAR FORMS IN LOGARITHMS: 7. Thue equations; 8. Thue-Mahler equations; 9. S-Unit equations; 10. Triangularly connected decomposable form equations; 11. Discriminant form equations; Part III. INTEGRAL AND RATIONAL POINTS ON CURVES: 12. Rational points on elliptic curves; 13. Integral points on elliptic curves; 14. Curves of genus greater than one; Appendices; Bibliography; Index.
Etiquetas de esta biblioteca: No hay etiquetas de esta biblioteca para este título. Inicie sesión para agregar etiquetas.
Valoración
    Valoración media: 0.0 (0 votos)
Existencias
Tipo de ítem Biblioteca de origen Signatura URL Estado Fecha de vencimiento Código de barras Reserva de ítems
Monografías 02. BIBLIOTECA CAMPUS PUERTO REAL
517.94/SMA/alg (Navegar estantería(Abre debajo)) Texto completo Disponible   Ubicación en estantería | Bibliomaps® 3741695602
Monografías 02. BIBLIOTECA CAMPUS PUERTO REAL
517.94/SMA/alg (Navegar estantería(Abre debajo)) Texto completo Prestado 31/01/2025 3741063700
Total de reservas: 0

Indice

Bibliografía: p. 231-239

Beginning with a brief introduction to algorithms and diophantine equations, this volume aims to provide a coherent modern 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.

Índice: Preface; 1. Introduction; Part I. BASIC SOLUTION TECHNIQUES: 2. Local methods; 3. Applications of local methods to diophantine equations; 4. Ternary quadratic forms; 5. Computational diophantine approximation; 6. Applications of the LLL-algorithm; Part II. METHODS USING LINEAR FORMS IN LOGARITHMS: 7. Thue equations; 8. Thue-Mahler equations; 9. S-Unit equations; 10. Triangularly connected decomposable form equations; 11. Discriminant form equations; Part III. INTEGRAL AND RATIONAL POINTS ON CURVES: 12. Rational points on elliptic curves; 13. Integral points on elliptic curves; 14. Curves of genus greater than one; Appendices; Bibliography; Index.

No hay comentarios en este titulo.

para aportar su opinión.

Con tecnología Koha