On the computation of totally real quartic fields of small discriminant-Reference-Cited by-同舟云学术

On the computation of totally real quartic fields of small discriminant

Published:1989 Issue:185 Volume:52 Page:161-174
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Buchmann Johannes,Ford David

Abstract

All totally real quartic fields of discriminant less than 10 6 {10^6} are computed. The method used to generate the fields is derived from Delone and Faddeev, with corrections and improvements. A new method for deciding field isomorphism is used to eliminate redundant examples. Integral bases and Galois groups are given for each field.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1989-52-185/S0025-5718-1989-0946599-1/S0025-5718-1989-0946599-1.pdf

Reference14 articles.

1. J. Buchmann & D. Ford, "Determining isomorphism of algebraic number fields." (Unpublished manuscript.)

2. Die Grundlehren der mathematischen Wissenschaften, Band 99;Cassels, J. W. S.,1971

3. Translations of Mathematical Monographs, Vol. 10;Delone, B. N.,1964

4. D. Ford, On the Computation of the Maximal Order in a Dedekind Domain, Ph.D. Dissertation, Ohio State University, 1978.

5. On the prime divisors of polynomials;Gerst, Irving;Amer. Math. Monthly,1971

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