Algorithmic Enumeration of Ideal Classes for Quaternion Orders Kirschmer, Markus Voight, John General Mathematics General Computer Science 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. Society for Industrial & Applied Mathematics (SIAM) 2010 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_6501 https://ris.uni-paderborn.de/record/42803 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> eng info:eu-repo/semantics/altIdentifier/doi/10.1137/080734467 info:eu-repo/semantics/altIdentifier/issn/0097-5397 info:eu-repo/semantics/altIdentifier/issn/1095-7111 info:eu-repo/semantics/closedAccess