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Dynamics on surfaces

Project description

The flatsurf package for SageMath adds functionality related to interval exchange transformations, translation surfaces, mapping classes and more. It is distributed as an external Python package. It installs on top of an existing Sage installation.

This package is based on SageMath and relies heavily on:

  • gmp or mpir for arbitrary precision arithmetic
  • PARI/GP for number field computations
  • GAP for finite groups representation and permutation groups


Installing flatsurf requires a working Sage installation (with Cython and gcc). Under most Linux distribution, you can install the package gcc (it might even be already installed by default). Under Mac OS X, get a working gcc by installing XCode from the Mac App Store.


The module is distributed on PyPI. You just need to run the following command:

$ sage -sh -c "pip install surface_dynamics --user"

Alternatively, you can download the source code (see below).


After installing flatsurf, check that it works by launching Sage and typing the following commands. You should get the same output as below.:

sage: from surface_dynamics.all import *
sage: o = Origami('(1,2)','(1,3)')
sage: print o
sage: o.sum_of_lyapunov_exponents()
sage: o.lyapunov_exponents_approx()
sage: o.veech_group()
Arithmetic subgroup with permutations of right cosets
sage: QuadraticStratum(1,1,1,1).orientation_cover()

sage: AbelianStrata(genus=3).list()
[H_3(4), H_3(3, 1), H_3(2^2), H_3(2, 1^2), H_3(1^4)]

sage: O = OrigamiDatabase()
sage: q = O.query(("stratum","=",AbelianStratum(2)), ("nb_squares","=",5))
sage: q.number_of()
sage: for o in q: print o, "\n"


Source code

The complete source code is available at


Your comments and help are welcome: For problems with Mac OS X:


  • Vincent Delecroix: maintainer
  • Samuel Lelièvre: contribution for origamis and permutation representative of quadratic strata
  • Charles Fougeron: Lyapunov exponents for strata coverings


  • flatsurf 0.3 is in version beta
  • flatsurf 0.2 was released on 2015-11-15.
  • flatsurf 0.1 was released on 2015-07-30.

Project details

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Files for surface-dynamics, version 0.3.beta2
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