Algorithmic enumeration of ideal classes for quaternion orders

Details Algorithmic enumeration of ideal classes for quaternion orders Algorithmic enumeration of ideal classes for quaternion orders

2008-08-28

arxiv.org/abs/0808.3833v3

Mathematics

Number Theory

40 pages, includes 2 tables; error corrected in Proposition 7.7

Scientific paper

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.

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