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Published in:
2014 | OriginalPaper | Chapter
Computation of Genus 0 Belyi Functions
Authors : Mark van Hoeij, Raimundas Vidunas
Published in: Mathematical Software – ICMS 2014
Publisher: Springer Berlin Heidelberg
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A tool package for computing genus 0 Belyi functions is presented, including simplification routines, computation of moduli fields, decompositions, dessins d’enfant. The main algorithm for computing the Belyi functions themselves is based on implied transformations of the hypergeometric differential equation to Fuchsian equations, preferably with few singular points. This gives a fast way to compute the Belyi functions (of degree 60 and beyond) with nearly regular branching patterns.