Constructing complete tables of quartic fields using Kummer theory

Authors:
Henri Cohen;Francisco Diaz Y Diaz;Michel Olivier
Affiliations:
Laboratoire A2X, U.M.R. 5465 du C.N.R.S., Université Bordeaux I, 351 Cours de la Libération, 33405 Talence Cedex, France;Laboratoire A2X, U.M.R. 5465 du C.N.R.S., Université Bordeaux I, 351 Cours de la Libération, 33405 Talence Cedex, France;Laboratoire A2X, U.M.R. 5465 du C.N.R.S., Université Bordeaux I, 351 Cours de la Libération, 33405 Talence Cedex, France
Venue:
Mathematics of Computation
Year:
2003

Citing 6
Cited 2

A course in computational algebraic number theory

A course in computational algebraic number theory
A fast algorithm to compute cubic fields

Mathematics of Computation
Computing ray class groups, conductors and discriminants

Mathematics of Computation
Tables of octic fields with a quartic subfield

Mathematics of Computation
Construction of Tables of Quartic Number Fields

ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
Gauss Composition and Generalizations

ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory

A Survey of Discriminant Counting

ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Enumeration of totally real number fields of bounded root discriminant

ANTS-VIII'08 Proceedings of the 8th international conference on Algorithmic number theory

Quantified Score

Hi-index	0.00

Visualization

Abstract

We explain how to construct tables of quartic fields of discriminant less than or equal to a given bound in an efficient manner using Kummer theory, instead of the traditional (and much less efficient) method using the geometry of numbers. As an application, we describe the computation of quartic fields of discriminant up to 107, the corresponding table being available by anonymous ftp.