Title:  Computing Dehn Twists and Geometric Intersection Numbers in Polynomial Time 
Authors:  Marcus Schaefer, Eric Sedgwick, Daniel Stefankovič 
Abstract:  Simple curves on surfaces are often represented as
sequences of intersections with a triangulation. However, there are much
more succinct ways of representing simple curves used by topologists,
including normal coordinates and DehnThurston coordinates. In these
representations, the length of a curve might be exponential in the size
of its representation. Nevertheless, we show that the following two basic tasks of computational topology, namely

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