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Computational Algebraic Number Theory : Oberwolfach Seminars - Michael E. Phost

Computational Algebraic Number Theory

Oberwolfach Seminars


Published: 1st September 1993
Ships: 15 business days
15 business days

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 D�sseldorf. 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

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.- x 1 The number field sieve.- x 2 KANT.- References.

ISBN: 9783764329136
ISBN-10: 3764329130
Series: Oberwolfach Seminars
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 90
Published: 1st September 1993
Publisher: Birkhauser Verlag AG
Country of Publication: CH
Dimensions (cm): 24.4 x 17.0  x 0.56
Weight (kg): 0.4