E. Bach, Explicit bounds for primality testing and related problems, Mathematics of Computation, vol.55, issue.191, pp.355-380, 1990.
DOI : 10.1090/S0025-5718-1990-1023756-8

J. Biasse and C. Fieker, A polynomial time algorithm for computing the HNF of a module over the integers of a number field, Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation, ISSAC '12, 2012.
DOI : 10.1145/2442829.2442844

W. Bosma, J. Cannon, and C. Playoust, The Magma Algebra System I: The User Language, Computational algebra and number theory, pp.3-4235, 1993.
DOI : 10.1006/jsco.1996.0125

J. Buchmann, A subexponential algorithm for the determination of class groups and regulators of algebraic number fields, Progr. Math, vol.91, pp.27-41, 1988.

L. Dembélé and J. Voight, Explicit methods for Hilbert modular forms. Elliptic curves, Hilbert modular forms and Galois deformations, pp.135-198, 2013.

A. Granville, Smooth numbers: computational number theory and beyond Algorithmic number theory: lattices, number fields, curves and cryptography, Math. Sci. Res. Inst. Publ, vol.44, pp.267-323, 2008.

J. L. Hafner and K. S. Mccurley, A rigorous subexponential algorithm for computation of class groups, Journal of the American Mathematical Society, vol.2, issue.4, pp.837-850, 1989.
DOI : 10.1090/S0894-0347-1989-1002631-0

W. M. Kantor and A. Lubotzky, The probability of generating a finite classical group, Geometriae Dedicata, vol.36, issue.1, pp.67-87, 1990.
DOI : 10.1007/BF00181465

U. Fincke and M. Pohst, Improved methods for calculating vectors of short length in a lattice, including a complexity analysis, Mathematics of Computation, vol.44, issue.170, pp.463-471, 1985.
DOI : 10.1090/S0025-5718-1985-0777278-8

R. Kannan, Improved algorithms for integer programming and related lattice problems, Proceedings of the fifteenth annual ACM symposium on Theory of computing , STOC '83, 1983.
DOI : 10.1145/800061.808749

S. Katok, Fuchsian groups. Chicago Lectures in Mathematics, 1992.

M. Kirschmer and J. Voight, Algorithmic Enumeration of Ideal Classes for Quaternion Orders, SIAM Journal on Computing, vol.39, issue.5, pp.1714-1747, 2010.
DOI : 10.1137/080734467

J. Klüners and S. Pauli, Computing residue class rings and Picard groups of orders, Journal of Algebra, vol.292, issue.1, pp.47-64, 2005.
DOI : 10.1016/j.jalgebra.2005.04.013

C. Maclachlan and A. W. Reid, The arithmetic of hyperbolic 3-manifolds, Graduate Texts in Mathematics, vol.219, 2003.
DOI : 10.1007/978-1-4757-6720-9

I. N. Sanov, Euclid's algorithm and one-sided prime factorization for matrix rings, Sibirsk. Mat. ? Z, vol.8, pp.846-852, 1967.
DOI : 10.1007/bf02196485

J. Serre, Trees. Translated from the French original by John Stillwell Corrected 2nd printing of the 1980 English translation, 2003.
URL : https://hal.archives-ouvertes.fr/tel-01260775

M. Vignéras, Arithmétique des algèbres de quaternions (French), Lecture notes in Mathematics, vol.800, 1980.

J. Voight, Computing fundamental domains for Fuchsian groups, Journal de Th??orie des Nombres de Bordeaux, vol.21, issue.2, pp.469-491, 2009.
DOI : 10.5802/jtnb.683

URL : http://arxiv.org/abs/0802.0196

J. Voight, The arithmetic of quaternion algebras In preparation. Accessible from the url http

U. Vollmer, An accelerated Buchmann algorithm for regulator computation in real quadratic fields Algorithmic number theory, Lecture Notes in Comput. Sci, pp.148-162, 2002.