| Titre : | Advanced topics in computational number theory |
| Auteurs : | Henri Cohen ; S. Axler |
| Type de document : | texte imprimé |
| Editeur : | New York : Springer-Verlag, 2000 |
| Collection : | Graduate texts in mathematics, num. 193 |
| ISBN/ISSN/EAN : | 978-0-387-98727-9 |
| Format : | 1 Vol. (XV-578 p.) / ill., couv. ill. / 24 cm |
| Langues originales: | |
| Index. décimale : | 512.7 (Théorie des nombres) |
| Catégories : | |
| Mots-clés: | Nombres(théorie des) |
| Résumé : |
The present book addresses a number of specific topics in computational number theory whereby the author is not attempting to be exhaustive in the choice of subjects. The book is organized as follows. Chapters 1 and 2 contain the theory and algorithms concerning Dedekind domains and relative extensions of number fields, and in particular the generalization to the relative case of the round 2 and related algorithms. Chapters 3, 4, and 5 contain the theory and complete algorithms concerning class field theory over number fields. The highlights are the algorithms for computing the structure of (Z_K/m)^*, of ray class groups, and relative equations for Abelian extensions of number fields using Kummer theory. Chapters 1 to 5 form a homogeneous subject matter which can be used for a 6 months to 1 year graduate course in computational number theory. The subsequent chapters deal with more miscellaneous subjects. Written by an authority with great practical and teaching experience in the field, this book together with the author's earlier book will become the standard and indispensable reference on the subject. |
| Note de contenu : |
Sommaire - 1: Fundamental Results and Algorithms in Dedekind Domains. - 2: Basic Relative Number Field Algorithms. - 3: The Fundamental Theorems of Global Class Field Theory. - 4: Computational Class Field Theory. - 5: Computing Defining Polynomials Using Kummer Theory. - 6: Computing Defining Polynomials Using Analytic Methods. - 7: Variations on Class and Unit Groups. - 8: Cubic Number Fields. - 9: Number Field Table Constructions. - App. A: Theoretical Results. - App. B: Electronic Information. - App. C: Tables 533 Bibliography. - Index of Notation 556. - Index of Algorithms. - General Index. |
| Côte titre : |
S8/58544 |
Exemplaires (1)
| Cote | Support | Localisation | Disponibilité |
|---|---|---|---|
| S8/58544 | Livre | Bibliothèque centrale | Disponible |
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