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Advanced topics in computational number theory (Cop. 2000) / Henri COHEN
Titre : Advanced topics in computational number theory Type de document : texte imprimé Auteurs : Henri COHEN, Auteur Editeur : New York : Springer-Verlag Année de publication : Cop. 2000 Collection : Graduate Texts in Mathematics, ISSN 0072-5285 num. 193 Importance : XV-578 p. ISBN/ISSN/EAN : 978-0-387-98727-9 Langues : Anglais (eng) Catégories : 11-01
11Y16
11YxxMots-clés : théorie des nombres Résumé : 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. Note de contenu : index, bibliogr. Advanced topics in computational number theory [texte imprimé] / Henri COHEN, Auteur . - Springer-Verlag, Cop. 2000 . - XV-578 p.. - (Graduate Texts in Mathematics, ISSN 0072-5285; 193) .
ISBN : 978-0-387-98727-9
Langues : Anglais (eng)
Catégories : 11-01
11Y16
11YxxMots-clés : théorie des nombres Résumé : 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. Note de contenu : index, bibliogr. Réservation
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Code-barres Cote Support Localisation Section Disponibilité 18098 COH/11/7574 Livre Recherche Salle Disponible Finite fields : theory, applications, and algorithms (cop. 1994) / Gary L. MULLEN
Titre : Finite fields : theory, applications, and algorithms : Second international conference on finite fields : theory, applications, and algorithms. August 17-21, 1993. Las Vegas, Nevada Type de document : texte imprimé Auteurs : Gary L. MULLEN, Editeur scientifique ; Peter Jau-Shyong SHIUE, Editeur scientifique Editeur : Providence, R. I. [Etats Unis] : American Mathematical Society Année de publication : cop. 1994 Collection : Contemporary mathematics, ISSN 0271-4132 num. 168 Importance : XXX-402 p. ISBN/ISSN/EAN : 978-0-8218-5183-8 Langues : Anglais (eng) Catégories : 05B05
11T02
11Y16
94A60
94B05Mots-clés : algèbre corps fini Finite fields : theory, applications, and algorithms : Second international conference on finite fields : theory, applications, and algorithms. August 17-21, 1993. Las Vegas, Nevada [texte imprimé] / Gary L. MULLEN, Editeur scientifique ; Peter Jau-Shyong SHIUE, Editeur scientifique . - American Mathematical Society, cop. 1994 . - XXX-402 p.. - (Contemporary mathematics, ISSN 0271-4132; 168) .
ISBN : 978-0-8218-5183-8
Langues : Anglais (eng)
Catégories : 05B05
11T02
11Y16
94A60
94B05Mots-clés : algèbre corps fini Réservation
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Code-barres Cote Support Localisation Section Disponibilité 7959 CON/168 Livre Recherche Salle Disponible Randomization, relaxation, and complexity in polynomial equation solving (cop. 2011) / Leonid GURVITS
Titre : Randomization, relaxation, and complexity in polynomial equation solving : Banff International Research Station Workshop on Randomization, Relaxation, and Complexity February 28–March 5, 2010 Banff, Ontario, Canada Type de document : texte imprimé Auteurs : Leonid GURVITS, Editeur scientifique ; Philippe PÉBAY, Editeur scientifique ; J. Maurice ROJAS, Editeur scientifique Editeur : Providence, R. I. [Etats Unis] : American Mathematical Society Année de publication : cop. 2011 Collection : Contemporary mathematics, ISSN 0271-4132 num. 556 Importance : VIII-217 p. ISBN/ISSN/EAN : 978-0-8218-5228-6 Langues : Anglais (eng) Catégories : 11Y16
12Y05
14M25
14P25
14Q20Mots-clés : théorie des nombres algorithme géométrie algébrique Résumé : This volume corresponds to the Banff International Research Station Workshop on Randomization, Relaxation, and Complexity, held from February 28–March 5, 2010 in Banff, Ontario, Canada. This volume contains a sample of advanced algorithmic techniques underpinning the solution of systems of polynomial equations. The papers are written by leading experts in algorithmic algebraic geometry and touch upon core topics such as homotopy methods for approximating complex solutions, robust floating point methods for clusters of roots, and speed-ups for counting real solutions. Vital related topics such as circuit complexity, random polynomials over local fields, tropical geometry, and the theory of fewnomials, amoebae, and coamoebae are treated as well. Recent advances on Smale’s 17th Problem, which deals with numerical algorithms that approximate a single complex solution in average-case polynomial time, are also surveyed. Note de contenu : références Randomization, relaxation, and complexity in polynomial equation solving : Banff International Research Station Workshop on Randomization, Relaxation, and Complexity February 28–March 5, 2010 Banff, Ontario, Canada [texte imprimé] / Leonid GURVITS, Editeur scientifique ; Philippe PÉBAY, Editeur scientifique ; J. Maurice ROJAS, Editeur scientifique . - American Mathematical Society, cop. 2011 . - VIII-217 p.. - (Contemporary mathematics, ISSN 0271-4132; 556) .
ISBN : 978-0-8218-5228-6
Langues : Anglais (eng)
Catégories : 11Y16
12Y05
14M25
14P25
14Q20Mots-clés : théorie des nombres algorithme géométrie algébrique Résumé : This volume corresponds to the Banff International Research Station Workshop on Randomization, Relaxation, and Complexity, held from February 28–March 5, 2010 in Banff, Ontario, Canada. This volume contains a sample of advanced algorithmic techniques underpinning the solution of systems of polynomial equations. The papers are written by leading experts in algorithmic algebraic geometry and touch upon core topics such as homotopy methods for approximating complex solutions, robust floating point methods for clusters of roots, and speed-ups for counting real solutions. Vital related topics such as circuit complexity, random polynomials over local fields, tropical geometry, and the theory of fewnomials, amoebae, and coamoebae are treated as well. Recent advances on Smale’s 17th Problem, which deals with numerical algorithms that approximate a single complex solution in average-case polynomial time, are also surveyed. Note de contenu : références Réservation
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Exemplaires
Code-barres Cote Support Localisation Section Disponibilité 18992 CON/556 Livre Recherche Salle Disponible