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
- PPL (Parma Polyhedra Library) and LattE (Lattice point Enumeration) for polytope computations
Installing surface_dynamics requires a working Sage installation (with Cython and gcc).
The module is distributed on PyPI. You just need to run the following command:
$ sage -pip install surface_dynamics [--user]
The –user option is optional and allows to install the module in your user space (and does not require administrator rights). Alternatively, you can install the development version using:
$ sage -pip install git+https://github.com/videlec/flatsurf-package [--user]
- short tutorial: http://www.labri.fr/perso/vdelecro/flatsurf.html
- complete module documentation: http://www.labri.fr/perso/vdelecro/surface-dynamics/
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]
The complete source code is available at:
Once you developed the source code you might want to install the package with:
$ sage -pip install . [--user] [--upgrade]
wher the options –user and –upgrade are optional. It can also be compiled inplace using:
$ sage -python setup.py build_ext --inplace
- flatsurf 0.3 was released on 2017-08-11 (as a Python package on PyPI)
- 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).
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