@article{8c43f27f3f1245a79ddb1097164e6269,
title = "Zariski density and computing in arithmetic groups",
abstract = "For n > 2, let Γn denote either SL(n, Z) or Sp(n, Z). We give a practical algorithm to compute the level of the maximal principal congruence subgroup in an arithmetic group H ≤ Γn. This forms the main component of our methods for computing with such arithmetic groups H. More generally, we provide algorithms for computing with Zariski dense groups in Γn. We use our GAP implementation of the algorithms to solve problems that have emerged recently for important classes of linear groups.",
author = "A. Detinko and Flannery, {D. L.} and A. Hulpke",
note = "The first and second authors received support from the Irish Research Council (grants {\textquoteleft}MatGpAlg{\textquoteright} and {\textquoteleft}MatGroups{\textquoteright}) and Science Foundation Ireland (grant 11/RFP.1/MTH/3212). The first author is also funded by a Marie Sklodowska-Curie Individual Fellowship grant under Horizon 2020 (EU Framework Programme for Research and Innovation). The third author was supported by Simons Foundation Collaboration Grant 244502.",
year = "2018",
month = mar,
doi = "10.1090/mcom/3236",
language = "English",
volume = "87",
pages = "967--986",
journal = "Mathematics of Computation",
issn = "0025-5718",
publisher = "American Mathematical Society",
number = "310",
}