sage-flatsurf
This is a software package for working with flat surfaces in SageMath. For the documentation, see the Links section below.
We aim for this package to support the investigation of geometric, algebraic and dynamical questions related to flat surfaces. By flat surface we mean a surface modeled on the plane with monodromy given by similarities of the plane, though current efforts are focused on translation surfaces and half-translation surfaces.
Currently, the package can:
- generate images of flat surfaces
- compute and plot straight-line trajectories
- deform translation surfaces through the GL(2,R) action and compute GL(2,R)-orbit closures (the latter requires libflatsurf)
- compute Delaunay decompositions.
SageMath, e-antic and exact-real are used to perform exact arithmetic.
This package is free software, released under the GPL v2 (see the COPYING
file). We welcome any help to improve the package and especially to broaden
the package's mathematical abilities.
The package is currently in active development. If you would like assistance in using it, please contact the authors.
Links
- Documentation: https://www.labri.fr/perso/vdelecro/sage-flatsurf/latest
- Page on the Python package index: https://pypi.org/project/sage-flatsurf/
- Development website: https://github.com/flatsurf/sage-flatsurf/
Installing the dependency
sage-flatsurf depends on the surface_dynamics package, which is distributed on PyPI and can be installed with the following command:
$ sage --pip install surface_dynamics [--user] [--upgrade]
The options --user and --upgrade are optional; --user is to
perform the installation in your user home instead of in the Sage sources;
--upgrade is to upgrade the package in case it is already installed.
Installing the package
Since sage-flatsurf is available on PyPI (see Links section above), the released version of sage-flatsurf can be installed by running the following command:
$ sage --pip install sage-flatsurf [--user] [--upgrade]
To install the development version of sage-flatsurf, run instead:
$ sage --pip install git+https://github.com/videlec/sage-flatsurf [--user] [--upgrade]
The options --user and --upgrade are optional; --user is to
perform the installation in your user home instead of in the Sage sources;
--upgrade is to upgrade the package in case it is already installed.
This might fail if Git is not installed on your computer (which could happen for example with certain versions of Sage in Windows). In this situation you have two options. Either you install Git. Or you download this project from the "Clone or download" drop-down menu above (you should get a zip file). Then you need to run the command:
$ sage --pip install TARBALL_NAME [--user] [--upgrade]
where TARBALL_NAME has to be replaced with the full path to your tarball.
Under Windows, it should be a Cygwin path and will look something like
/cygdrive/c/Users/You/Downloads/sage-flatsurf-master.zip.
Then you should be able to use the following within Sage:
sage: import flatsurf.geometry.similarity_surface_generators as sfg sage: T = sfg.translation_surfaces.regular_octagon() sage: T Translation surface built from 1 polygon sage: T.stratum() H_2(2)
To uninstall the package, you can do:
$ sage --pip uninstall flatsurf
Run the tests
Running the tests of a specific file or directory is done by running:
$ sage -t --force-lib ARG
where ARG is either a directory or file. In particular, to test all the
files in the module just do:
$ sage -t --force-lib flatsurf
Tests on the master branch are automatically run through Travis-CI.
Related projects
There are several related projects
- surface_dynamics (SageMath module): more focused on dynamics (interval exchanges)
- veerer (Python module): to handle specific triangulations of half-translation surfaces
- libflatsurf: (C++ library with Python interface) computing GL(2,R)-orbit closures of translation surfaces
Primary Contributors
- Vincent Delecroix (Bordeaux)
- Pat Hooper (City College of New York and CUNY Graduate Center)
We welcome others to contribute.
Acknowledgements
- This software project was created during a thematic semester at ICERM.
- Hooper's contribution to the project has been supported by the National Science Foundation under Grant Number DMS-1500965. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.
- Delecroix's contribution to the project has been supported by OpenDreamKit, Horizon 2020 European Research Infrastructures project #676541.