Let G be a finite group. By Riemann's Existence Theorem, braid orbits of generating systems of G with product 1 correspond to irreducible families of covers of the Riemann sphere with monodromy group G. Thus, many problems on algebraic curves require the computation of braid orbits. In this paper, we describe an implementation of this computation. We discuss several applications, including the classification of irreducible families of indecomposable rational functions with exceptional monodromy group.
"A GAP Package for Braid Orbit Computation and Applications." Experiment. Math. 12 (4) 385 - 394, 2003.