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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)



Algorithms in algebraic number theory

Author: H. W. Lenstra
Journal: Bull. Amer. Math. Soc. 26 (1992), 211-244
MSC (2000): Primary 11Y40; Secondary 11R27, 11R29
MathSciNet review: 1129315
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Abstract: In this paper we discuss the basic problems of algorithmic algebraic number theory. The emphasis is on aspects that are of interest from a purely mathematical point of view, and practical issues are largely disregarded. We describe what has been done and, more importantly, what remains to be done in the area. We hope to show that the study of algorithms not only increases our understanding of algebraic number fields but also stimulates our curiosity about them. The discussion is concentrated of three topics: the determination of Galois groups, the determination of the ring of integers of an algebraic number field, and the computation of the group of units and the class group of that ring of integers.

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Keywords: Algebraic number theory, algorithms, complexity theory
Article copyright: © Copyright 1992 American Mathematical Society