@article{Lenstra1992AlgorithmsIA,
title={Algorithms in algebraic number theory},
author={H. Lenstra},
journal={Bulletin of the American Mathematical Society},
year={1992},
volume={26},
pages={211-244}
}

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 urea. We hope to show that the study of algorithms not only increases our understanding of algebraic number fields but also stimulates our curiosity about themĀ