surface-dynamics 0.3.beta3

Dynamics on surfaces

The surface_dynamics 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

Prerequisites

Installing surface_dynamics 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.

Installation

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).

Documentation

• https://pythonhosted.org/surface_dynamics/

• http://www.labri.fr/perso/vdelecro/flatsurf.html

Check

After installing surface_dynamics, 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
(1,2)(3)
(1,3)(2)
sage: o.sum_of_lyapunov_exponents()
4/3
sage: o.lyapunov_exponents_approx()
[0.33441823619678734]
sage: o.veech_group()
Arithmetic subgroup with permutations of right cosets
 S2=(2,3)
 S3=(1,2,3)
 L=(1,2)
 R=(1,3)
sage: QuadraticStratum(1,1,1,1).orientation_cover()
H_5(2^4)^odd

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()
2
sage: for o in q: print o, "\n"
(1)(2)(3)(4,5)
(1,2,3,4)(5)

(1)(2)(3,4,5)
(1,2,3)(4)(5)

sage: Q12_reg = QuadraticStratum(12).regular_component()
sage: Q12_reg.lyapunov_exponents_H_plus()
[0.6671, 0.4506, 0.2372, 0.08841]
sage: Q12_reg.lyapunov_exponents_H_minus()
[1.001, 0.6669, 0.45018, 0.3139, 0.23218, 0.12143, 0.08594]

Source code

The complete source code is available at https://github.com/videlec/flatsurf-package

Contact

Your comments and help are welcome: [e-mail] For problems with Mac OS X: [e-mail]

Authors

• Vincent Delecroix: maintainer

• Samuel Lelièvre: contribution for origamis and permutation representative of quadratic strata

• Charles Fougeron: Lyapunov exponents for strata coverings

Versions

• flatsurf 0.3 is in version beta

• flatsurf 0.2 was released on 2015-11-15 (as a Sage spkg).

• flatsurf 0.1 was released on 2015-07-30 (as a Sage spkg).