---
_id: '42803'
abstract:
- lang: eng
  text: 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.
author:
- first_name: Markus
  full_name: Kirschmer, Markus
  id: '82258'
  last_name: Kirschmer
- first_name: John
  full_name: Voight, John
  last_name: Voight
citation:
  ama: Kirschmer M, Voight J. Algorithmic Enumeration of Ideal Classes for Quaternion
    Orders. <i>SIAM Journal on Computing</i>. 2010;39(5):1714-1747. doi:<a href="https://doi.org/10.1137/080734467">10.1137/080734467</a>
  apa: Kirschmer, M., &#38; Voight, J. (2010). Algorithmic Enumeration of Ideal Classes
    for Quaternion Orders. <i>SIAM Journal on Computing</i>, <i>39</i>(5), 1714–1747.
    <a href="https://doi.org/10.1137/080734467">https://doi.org/10.1137/080734467</a>
  bibtex: '@article{Kirschmer_Voight_2010, title={Algorithmic Enumeration of Ideal
    Classes for Quaternion Orders}, volume={39}, DOI={<a href="https://doi.org/10.1137/080734467">10.1137/080734467</a>},
    number={5}, journal={SIAM Journal on Computing}, publisher={Society for Industrial
    &#38; Applied Mathematics (SIAM)}, author={Kirschmer, Markus and Voight, John},
    year={2010}, pages={1714–1747} }'
  chicago: 'Kirschmer, Markus, and John Voight. “Algorithmic Enumeration of Ideal
    Classes for Quaternion Orders.” <i>SIAM Journal on Computing</i> 39, no. 5 (2010):
    1714–47. <a href="https://doi.org/10.1137/080734467">https://doi.org/10.1137/080734467</a>.'
  ieee: 'M. Kirschmer and J. Voight, “Algorithmic Enumeration of Ideal Classes for
    Quaternion Orders,” <i>SIAM Journal on Computing</i>, vol. 39, no. 5, pp. 1714–1747,
    2010, doi: <a href="https://doi.org/10.1137/080734467">10.1137/080734467</a>.'
  mla: Kirschmer, Markus, and John Voight. “Algorithmic Enumeration of Ideal Classes
    for Quaternion Orders.” <i>SIAM Journal on Computing</i>, vol. 39, no. 5, Society
    for Industrial &#38; Applied Mathematics (SIAM), 2010, pp. 1714–47, doi:<a href="https://doi.org/10.1137/080734467">10.1137/080734467</a>.
  short: M. Kirschmer, J. Voight, SIAM Journal on Computing 39 (2010) 1714–1747.
date_created: 2023-03-07T08:49:35Z
date_updated: 2023-04-04T09:25:08Z
department:
- _id: '102'
doi: 10.1137/080734467
extern: '1'
intvolume: '        39'
issue: '5'
keyword:
- General Mathematics
- General Computer Science
language:
- iso: eng
page: 1714-1747
publication: SIAM Journal on Computing
publication_identifier:
  issn:
  - 0097-5397
  - 1095-7111
publication_status: published
publisher: Society for Industrial & Applied Mathematics (SIAM)
status: public
title: Algorithmic Enumeration of Ideal Classes for Quaternion Orders
type: journal_article
user_id: '93826'
volume: 39
year: '2010'
...