Algorithmic enumeration of ideal classes for quaternion orders
Number Theory
2014-11-19 v4
Abstract
We provide algorithms to count and enumerate representatives of the (right) ideal classes of an Eichler order in a quaternion algebra defined over a number field. We analyze the run time of these algorithms and consider several related problems, including the computation of two-sided ideal classes, isomorphism classes of orders, connecting ideals for orders, and ideal principalization. We conclude by giving the complete list of definite Eichler orders with class number at most 2.
Cite
@article{arxiv.0808.3833,
title = {Algorithmic enumeration of ideal classes for quaternion orders},
author = {Markus Kirschmer and John Voight},
journal= {arXiv preprint arXiv:0808.3833},
year = {2014}
}
Comments
39 pages, includes 2 tables; corrections made to Table 8.3