Algorithmic Enumeration of Ideal Classes for Quaternion Orders
M. Kirschmer, J. Voight, SIAM Journal on Computing 39 (2010) 1714–1747.
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Journal Article
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| English
Author
Kirschmer, MarkusLibreCat;
Voight, John
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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.
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Journal Title
SIAM Journal on Computing
Volume
39
Issue
5
Page
1714-1747
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Kirschmer M, Voight J. Algorithmic Enumeration of Ideal Classes for Quaternion Orders. SIAM Journal on Computing. 2010;39(5):1714-1747. doi:10.1137/080734467
Kirschmer, M., & Voight, J. (2010). Algorithmic Enumeration of Ideal Classes for Quaternion Orders. SIAM Journal on Computing, 39(5), 1714–1747. https://doi.org/10.1137/080734467
@article{Kirschmer_Voight_2010, title={Algorithmic Enumeration of Ideal Classes for Quaternion Orders}, volume={39}, DOI={10.1137/080734467}, number={5}, journal={SIAM Journal on Computing}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Kirschmer, Markus and Voight, John}, year={2010}, pages={1714–1747} }
Kirschmer, Markus, and John Voight. “Algorithmic Enumeration of Ideal Classes for Quaternion Orders.” SIAM Journal on Computing 39, no. 5 (2010): 1714–47. https://doi.org/10.1137/080734467.
M. Kirschmer and J. Voight, “Algorithmic Enumeration of Ideal Classes for Quaternion Orders,” SIAM Journal on Computing, vol. 39, no. 5, pp. 1714–1747, 2010, doi: 10.1137/080734467.
Kirschmer, Markus, and John Voight. “Algorithmic Enumeration of Ideal Classes for Quaternion Orders.” SIAM Journal on Computing, vol. 39, no. 5, Society for Industrial & Applied Mathematics (SIAM), 2010, pp. 1714–47, doi:10.1137/080734467.
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