Articles liés à Advanced Topics in Computational Number Theory
Synopsis
Preliminary Text. Do not use. 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. 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.
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Présentation de l'éditeur
This book addresses a number of specific topics in computational number theory centered on class field theory and relative extensions of number fields. Most of the material is new from the algorithmic standpoint. 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, 5, and 6 contain the theory and complete algorithms concerning class field theory over number fields. The highlights are the algorithms for computing the structure of (zk/m)*, of ray class groups, and relative equations for Abelian extensions based on complex multiplication or Stark's conjectures. Together with Chapter 10, which contains complete proofs of several results used in the rest of the book that cannot easily be found in the existing literature, Chapters 1 to 6 form a homogeneous subject matter, which can be used for a 6-month to 1-year graduate course in computational number theory. The other 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, A Course in Computational Algebraic Number Theory (GTM 138), will become the standard and indispensable reference on the subject.
Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.
- ÉditeurSpringer
- Date d'édition2012
- ISBN 10 1461264197
- ISBN 13 9781461264194
- ReliureBroché
- Langueanglais
- Nombre de pages600
- Coordonnées du fabricantnon disponible
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Advanced Topics in Computational Number Theory
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Springer New York, 2012
ISBN 10 : 1461264197
ISBN 13 : 9781461264194
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Etat : New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Written by an authority with great practical and teaching experience in the field, this book addresses a number of topics in computational number theory. Chapters one through five form a homogenous subject matter suitable for a six-month or year-long cou. N° de réf. du vendeur 4189074
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Advanced Topics in Computational Number Theory (Graduate Texts in Mathematics)
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Advanced Topics in Computational Number Theory
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Advanced Topics in Computational Number Theory
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Springer New York Okt 2012, 2012
ISBN 10 : 1461264197
ISBN 13 : 9781461264194
Neuf
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Vendeur : BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Allemagne
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Taschenbuch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Written by an authority with great practical and teaching experience in the field, this book addresses a number of topics in computational number theory. Chapters one through five form a homogenous subject matter suitable for a six-month or year-long course in computational number theory. The subsequent chapters deal with more miscellaneous subjects. 600 pp. Englisch. N° de réf. du vendeur 9781461264194
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Advanced Topics in Computational Number Theory
Edité par
Springer New York, Springer US Okt 2012, 2012
ISBN 10 : 1461264197
ISBN 13 : 9781461264194
Neuf
Taschenbuch
Vendeur : buchversandmimpf2000, Emtmannsberg, BAYE, Allemagne
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Taschenbuch. Etat : Neu. Neuware -The computation of invariants of algebraic number fields such as integral bases, discriminants, prime decompositions, ideal class groups, and unit groups is important both for its own sake and for its numerous applications, for example, to the solution of Diophantine equations. The practical com pletion of this task (sometimes known as the Dedekind program) has been one of the major achievements of computational number theory in the past ten years, thanks to the efforts of many people. Even though some practical problems still exist, one can consider the subject as solved in a satisfactory manner, and it is now routine to ask a specialized Computer Algebra Sys tem such as Kant/Kash, liDIA, Magma, or Pari/GP, to perform number field computations that would have been unfeasible only ten years ago. The (very numerous) algorithms used are essentially all described in A Course in Com putational Algebraic Number Theory, GTM 138, first published in 1993 (third corrected printing 1996), which is referred to here as [CohO]. That text also treats other subjects such as elliptic curves, factoring, and primality testing. Itis important and natural to generalize these algorithms. Several gener alizations can be considered, but the most important are certainly the gen eralizations to global function fields (finite extensions of the field of rational functions in one variable overa finite field) and to relative extensions ofnum ber fields. As in [CohO], in the present book we will consider number fields only and not deal at all with function fields.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 600 pp. Englisch. N° de réf. du vendeur 9781461264194
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Advanced Topics in Computational Number Theory
Edité par
Springer New York, Springer US, 2012
ISBN 10 : 1461264197
ISBN 13 : 9781461264194
Neuf
Taschenbuch
Vendeur : AHA-BUCH GmbH, Einbeck, Allemagne
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Taschenbuch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - The computation of invariants of algebraic number fields such as integral bases, discriminants, prime decompositions, ideal class groups, and unit groups is important both for its own sake and for its numerous applications, for example, to the solution of Diophantine equations. The practical com pletion of this task (sometimes known as the Dedekind program) has been one of the major achievements of computational number theory in the past ten years, thanks to the efforts of many people. Even though some practical problems still exist, one can consider the subject as solved in a satisfactory manner, and it is now routine to ask a specialized Computer Algebra Sys tem such as Kant/Kash, liDIA, Magma, or Pari/GP, to perform number field computations that would have been unfeasible only ten years ago. The (very numerous) algorithms used are essentially all described in A Course in Com putational Algebraic Number Theory, GTM 138, first published in 1993 (third corrected printing 1996), which is referred to here as [CohO]. That text also treats other subjects such as elliptic curves, factoring, and primality testing. Itis important and natural to generalize these algorithms. Several gener alizations can be considered, but the most important are certainly the gen eralizations to global function fields (finite extensions of the field of rational functions in one variable overa finite field) and to relative extensions ofnum ber fields. As in [CohO], in the present book we will consider number fields only and not deal at all with function fields. N° de réf. du vendeur 9781461264194
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Advanced Topics in Computational Number Theory
Edité par
Springer-Verlag New York Inc., 2012
ISBN 10 : 1461264197
ISBN 13 : 9781461264194
Neuf
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Advanced Topics in Computational Number Theory
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Advanced Topics in Computational Number Theory
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Advanced Topics in Computational Number Theory
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Etat : New. Print on Demand pp. 600 49:B&W 6.14 x 9.21 in or 234 x 156 mm (Royal 8vo) Perfect Bound on White w/Gloss Lam. N° de réf. du vendeur 55052536
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