Computational Algebraic Number Theory

M. E. Pohst

ISBN 10: 3764329130 / ISBN 13: 9783764329136

Editore: Birkhäuser Basel, Birkhäuser Basel Sep 1993, 1993

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This item is printed on demand - Print on Demand Titel. Neuware -Computational algebraic number theory has been attracting broad interest in the last few years due to its potential applications in coding theory and cryptography. For this reason, the Deutsche Mathematiker Vereinigung initiated an introductory graduate seminar on this topic in Düsseldorf. The lectures given there by the author served as the basis for this book which allows fast access to the state of the art in this area. Special emphasis has been placed on practical algorithms - all developed in the last five years - for the computation of integral bases, the unit group and the class group of arbitrary algebraic number fields. Contents: Introduction ¿ Topics from finite fields ¿ Arithmetic and polynomials ¿ Factorization of polynomials ¿ Topics from the geometry of numbers ¿ Hermite normal form ¿ Lattices ¿ Reduction ¿ Enumeration of lattice points ¿ Algebraic number fields ¿ Introduction ¿ Basic Arithmetic ¿ Computation of an integral basis ¿ Integral closure ¿ Round-Two-Method ¿ Round-Four-Method ¿ Computation of the unit group ¿ Dirichlet's unit theorem and a regulator bound ¿ Two methods for computing r independent units ¿ Fundamental unit computation ¿ Computation of the class group ¿ Ideals and class number ¿ A method for computing the class group ¿ Appendix ¿ The number field sieve ¿ KANT ¿ References ¿ IndexSpringer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 104 pp. Englisch.

Codice articolo 9783764329136

Dati bibliografici

• Titolo: Computational Algebraic Number Theory
• Editore: Birkhäuser Basel, Birkhäuser Basel Sep 1993
• Data di pubblicazione: 1993
• Lingua: Inglese
• ISBN 10: 3764329130
• ISBN 13: 9783764329136
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 244 L x 170 A x 7 P (millimetri) 244 millimetri di larghezza per 170 millimetri di altezza per 7 millimetri di profondità
• Peso: 196 grammi

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Riassunto

Computational algebraic number theory has been attracting broad interest in the last few years due to its potential applications in coding theory and cryptography. For this reason, the Deutsche Mathematiker Vereinigung initiated an introductory graduate seminar on this topic in Düsseldorf. The lectures given there by the author served as the basis for this book which allows fast access to the state of the art in this area. Special emphasis has been placed on practical algorithms - all developed in the last five years - for the computation of integral bases, the unit group and the class group of arbitrary algebraic number fields. Contents: Introduction Topics from finite fields Arithmetic and polynomials Factorization of polynomials Topics from the geometry of numbers Hermite normal form Lattices Reduction Enumeration of lattice points Algebraic number fields Introduction Basic Arithmetic Computation of an integral basis Integral closure Round-Two-Method Round-Four-Method Computation of the unit group Dirichlet's unit theorem and a regulator bound Two methods for computing r independent units Fundamental unit computation Computation of the class group Ideals and class number A method for computing the class group Appendix The number field sieve KANT References Index

Contenuti

Intorduction.- Topics from finite field.- Topics from the geometry of number.- Algebraic number field.- Computation of an integral basis.- Computation of the unit group.- Computation of the class group.- § 1 The number field sieve.- § 2 KANT.- References.