Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Improved computation of fundamental domains for arithmetic Fuchsian
  groups   The fundamental domain of an arithmetic Fuchsian group $\Gamma$ reveals a lot
of interesting information about the group. An algorithm to efficiently compute
this fundamental domain in practice was given by Voight, and it was later
expanded by Page to the case of arithmetic Kleinian groups. Page's version
featured a probabilistic enumeration of group elements, which performed
significantly better than Voight's deterministic enumeration. In this paper, we
improve on the geometric algorithms described by Voight, and specialize Page's
enumeration down to Fuchsian groups, to produce a final algorithm that is much
more efficient. Optimal choices of constants in the enumeration are given by
heuristics, which are supported by large amounts of data. This algorithm has
been implemented in PARI/GP, and we demonstrate its practicality by comparing
running times versus the live Magma implementation of Voight's algorithm.

12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: stat
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci