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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Computing ideal classes representatives in quaternion algebras
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by Ariel Pacetti and Nicolás Sirolli PDF
Math. Comp. 83 (2014), 2479-2507 Request permission

Abstract:

Let $K$ be a totally real number field and let $B$ be a totally definite quaternion algebra over $K$. Given a set of representatives for ideal classes for a maximal order in $B$, we show how to construct in an efficient way a set of representatives of ideal classes for any Bass order in $B$. The algorithm does not require any knowledge of class numbers, and improves the equivalence checking process by using a simple calculation with global units. As an application, we compute ideal classes representatives for an order of discriminant $30$ in an algebra over the real quadratic field $\mathbb {Q}[\sqrt {5}]$.
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Additional Information
  • Ariel Pacetti
  • Affiliation: Departamento de Matemática, Universidad de Buenos Aires - Pabellón I, Ciudad Universitaria (C1428EGA), Buenos Aires, Argentina
  • MR Author ID: 759256
  • Email: apacetti@dm.uba.ar
  • Nicolás Sirolli
  • Affiliation: Departamento de Matemática, Universidad de Buenos Aires - Pabellón I, Ciudad Universitaria (C1428EGA), Buenos Aires, Argentina
  • MR Author ID: 1067127
  • ORCID: 0000-0002-0603-4784
  • Email: nsirolli@dm.uba.ar
  • Received by editor(s): June 20, 2011
  • Received by editor(s) in revised form: January 6, 2012, November 30, 2012, and January 21, 2013
  • Published electronically: January 9, 2014
  • Additional Notes: The first author was partially supported by PIP 2010-2012 GI and UBACyT X867
    The second author was partially supported by a CONICET Ph.D. Fellowship
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 83 (2014), 2479-2507
  • MSC (2010): Primary 11R52
  • DOI: https://doi.org/10.1090/S0025-5718-2014-02796-8
  • MathSciNet review: 3223343