Suppose I have a subgroup of $SL(2, \mathbb{Z})$ given by explicit matrix generators, and my goal in life is to construct a Dirichlet domain (for, say, everyone's favorite basepoint $\sqrt{-1}$). Is there any known estimate on how big a piece of the orbit I need to compute?
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asked Aug 30, 2016 at 15:39
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$\begingroup$ Wow, someone downvoted this question! It must be really trivial... $\endgroup$– Igor RivinCommented Aug 31, 2016 at 14:26
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$\begingroup$ Igor: Did you check J. Gilman, Algorithms, complexity and discreteness criteria in PSL(2, C), J. Anal. Math. 73 (1997), pp. 91–114. There she estimates complexity of Riley's algorithm, but maybe only from below, I do not remember... $\endgroup$– MishaCommented Sep 1, 2016 at 4:13
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