sage-flatsurf: Flat Surfaces in SageMath#
sage-flatsurf is a Python package for working with flat surfaces in SageMath.
We aim for sage-flatsurf 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.
The preferred way to install software should be to use your package manager (e.g. apt-get on Debian or Ubuntu, pacman on Arch Linux, brew on MacOS, etc). However, as of this writing, sage-flatsurf has not been picked up by any of the major distributions yet.
We therefore recommend to install sage-flatsurf with the Mamba package manager.
Detailed installation instructions:
If you are planning to work on the sage-flatsurf source code, you can also build sage-flatsurf from source. For this, please have a look at our Developer’s Guide.
A Tour of sage-flatsurf#
Demos of some of the capabilities of sage-flatsurf:
- Defining Surfaces
- Graphics Configuration
- The GL(2,R) Action, the Veech Group, Delaunay Decomposition
- Relative Period Deformations
- Working with Saddle Connections
- Exploring Orbit Closures
- Siegel-Veech Constants
- Straight-Line Flow
- Notes from the Warwick EPSRC Symposium on “Computation in geometric topology”
- The flatsurf.geometry Package
- The flatsurf.graphical Package