Timeline for Is there an algorithm to compute efficiently the dessin d'enfant from a Belyi pair?
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Mar 26, 2014 at 12:01 | vote | accept | Dima Sustretov | ||
| Nov 28, 2013 at 23:40 | comment | added | John Voight | If instead you are given the finite index subgroup (or equivalently, the permutation triple), then it is much easier to write down the combinatorial-topological data given by the dessin as a graph: it is explained in Chapter 4 of Girondo, Gonzalez-Diez "Introduction to Compact Riemann Surfaces and Dessins d'Enfants", and presumably elsewhere: you just read off the dessin from the monodromy. In fact, you can do this in a conformally correct way on the desired surface: see another one of my preprints (arxiv.org/abs/1311.2081), where there are lots of pictures. | |
| Nov 28, 2013 at 23:37 | comment | added | John Voight | Hopefully our preprint (arxiv.org/abs/1311.2529) addresses your question. If you are given equations, you "just" need to do some numerical homotopy: choose a base point and trace the preimages of loops on the curve around 0, 1, oo. This has been implemented by Kroeker (github.com/jakobkroeker/HMAC) and Bartholdi (github.com/laurentbartholdi/img). I don't think Bertini or PHCPack will give this to you directly, though they are similar in spirit. | |
| Nov 13, 2013 at 21:13 | history | answered | Alexandre Eremenko | CC BY-SA 3.0 |