## 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 $\mathbb {Q}[\sqrt {5}]$.## References

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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