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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
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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.
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Computational Algebraic Number Theory (Oberwolfach Seminars, 21)
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Computational algebraic number theory. DMV-Seminar; Bd. 21.
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Computational algebraic number theory Michael E. Pohst. DMV Seminar 21.
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Computational Algebraic Number Theory
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Computational Algebraic Number Theory
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Basel, Boston, Berlin: Birkhäuser Verlag, 1993
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Condizione: Gut. 88 Seiten Zustand: Einband etwas berieben // DMV Seminar 21 /// Versand gratis Innerhalb Deutschlands - Portofrei in Deutschland- ab 20 Euro mit Post ID - Gratisversand deutschlandweit innerhalb Deutschlands gratis Versand -Versandkostenfrei innerhalb Deutschlands /// Sprache: Englisch Gewicht in Gramm: 200 gr.8°, 24,0 x 17,0 cm, Broschur bzw. Taschenbuch. Codice articolo 270934
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Computational Algebraic Number Theory
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Kartoniert / Broschiert. Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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 sem. Codice articolo 5279015
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Computational Algebraic Number Theory
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Springer, Basel, Birkhäuser Basel, Birkhäuser Sep 1993, 1993
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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - 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 - Index 90 pp. Englisch. Codice articolo 9783764329136
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Computational Algebraic Number Theory
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Taschenbuch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Codice articolo 9783764329136
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Computational Algebraic Number Theory (Oberwolfach Seminars, 21)
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