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Welcome to the sage-flatsurf wiki!

We are developing develop a package for translation surfaces within Sage.

Features:

• Support for translation surfaces, half-translation surfaces, dilation surfaces, half-dilation surfaces, Euclidean cone surfaces and similarity surfaces.
• Support for plotting surfaces, saddle connections, points.

Demonstrations:

Demonstrations of FlatSurf are included in the "examples/" directory.

• Defining surfaces
• Straight-line flow
• Linear action and the Delaunay decomposition
• Saddle connections
• Relative Period Deformations
• Graphics configuration

Newly Implemented Features:

• Delaunay decomposition/triangulation for finite surfaces.
• Delaunay decompositions for infinite surfaces.
• In place canonicalization of translation surfaces.
• computing saddle connections

Wishlist:

• Good cylinder class.
• Support infinite polygons (for example arising from high order poles of differentials).
• Computing 2-dimensional rel-deformation spaces.
• L-infinity Delaunay decompositions.
• In place canonicalization of half-translation surfaces. (Other types of surfaces?)
• finding Veech group elements.
• constructing mapping tori from pseudo-Anosov elements. (Some progress through integration with Mark Bell's Flipper)
• More contributors
• More items to add to the wishlist

Things to integrate:

• Ronen Mukamel program to compute Veech groups http://www.stanford.edu/~ronen/
• Vincent Delecroix package at http://www.labri.fr/perso/vdelecro/flatsurf-5.12.tar
• Anton Zorich, Charles Fougeron, Alex Eskin, ...

Longer term goals:

• gui interface (not pressing)