Office of Academic Resources
Chulalongkorn University
Chulalongkorn University

Home / Help

AuthorPohst, Michael E. author
TitleComputational Algebraic Number Theory [electronic resource] / by Michael E. Pohst
ImprintBasel : Birkhรคuser Basel : Imprint: Birkhรคuser, 1993
Connect tohttp://dx.doi.org/10.1007/978-3-0348-8589-8
Descript X, 90 p. 1 illus. online resource

SUMMARY

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 Dรผsseldorf. 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 โ{128}ข Topics from finite fields โ{128}ข Arithmetic and polynomials โ{128}ข Factorization of polynomials โ{128}ข Topics from the geometry of numbers โ{128}ข Hermite normal form โ{128}ข Lattices โ{128}ข Reduction โ{128}ข Enumeration of lattice points โ{128}ข Algebraic number fields โ{128}ข Introduction โ{128}ข Basic Arithmetic โ{128}ข Computation of an integral basis โ{128}ข Integral closure โ{128}ข Round-Two-Method โ{128}ข Round-Four-Method โ{128}ข Computation of the unit group โ{128}ข Dirichlet's unit theorem and a regulator bound โ{128}ข Two methods for computing r independent units โ{128}ข Fundamental unit computation โ{128}ข Computation of the class group โ{128}ข Ideals and class number โ{128}ข A method for computing the class group โ{128}ข Appendix โ{128}ข The number field sieve โ{128}ข KANT โ{128}ข References โ{128}ข Index


CONTENT

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 -- ยง 1 The number field sieve -- ยง 2 KANT -- References


Mathematics Science Number theory Mathematics Number Theory Science general



Location



Office of Academic Resources, Chulalongkorn University, Phayathai Rd. Pathumwan Bangkok 10330 Thailand

Contact Us

Tel. 0-2218-2929,
0-2218-2927 (Library Service)
0-2218-2903 (Administrative Division)
Fax. 0-2215-3617, 0-2218-2907

Social Network

  line

facebook   instragram