POLYNOMIAL COMPLEXITY OF THE GILMAN{MASKIT DISCRETENESS ALGORITHM
The main result of this paper is a polynomial bound for the computational complexity of an algorithm to determine whether or not a non-elementary two-generator subgroup of PSL (2; R) is discrete, that is, an algorithm to determine whether such a subgroup is Fuchsian. The proof that there exists such a bound uses techniques from both hyperbolic geometry and symbolic computation.