Computational Algebraic Number Theory

Pohst Michael

ISBN 10: 3764329130 / ISBN 13: 9783764329136

Verlag: Springer, 1993

Print on Demand pp. 104 67:B&W 6.69 x 9.61 in or 244 x 170 mm (Pinched Crown) Perfect Bound on White w/Gloss Lam. Bestandsnummer des Verkäufers 5825690

Inhaltsangabe:

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

Reseña del editor: 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

Bibliografische Details

Titel: Computational Algebraic Number Theory
Verlag: Springer
Erscheinungsdatum: 1993
Einband: Softcover
Zustand: New