# Sébastien Labbé’s Research Code¶

This is an optional package for SageMath containing code I wrote for research. It contains modules on the following topics.

Discrete dynamical systems
diophantine approximation, Markov transformations, Wang tilings, Lyapunov exponents, matrix cocycles, multidimensional continued fraction algorithms, polyhedron exchange transformations,
Combinatorics
2d substitutions, bispecial factors, bond percolation, Dyck word in 3D, words, Joyal bijection, languages, Oldenburger sequence, ostrowski numeration, partial injections,
Digital geometry
Christoffel graph, discrete subset, discrete plane, double square tiles, polyhedron partitions,
Vizualization
tikzpicture
Miscellaneous
analyze Sage build time, fruit Python classes example, ranking scale

### Prerequisites¶

Installing slabbe requires a working SageMath installation (with Cython and gcc). Depending on the usage, it might be necessary to install the optional packages dot2tex, glucose, cryptominisat and latte_int:

sage -i dot2tex glucose cryptominisat latte_int


as well as the external packages Graphviz and Gurobi. See this thematic tutorial to use Gurobi in SageMath.

### Installation¶

The module is distributed on PyPI and is easily installed through the Python package manager pip:

sage -pip install slabbe


To install the module in your user space (which does not require administrator rights):

sage -pip install slabbe --user


Usage:

sage: from slabbe import *


### It builds on SageMath¶

It depends heavily on the SageMath library as it uses the following modules: combinat, functions, geometry, graphs, matrix, misc, modules, numerical, parallel, plot, probability, rings, sat, sets, structure, symbolic.

SageMath is free open source math software that supports research and teaching in algebra, geometry, number theory, cryptography, and related areas.

### Follows the Best practices for scientific computing¶

It follows as much as possible the SageMath general conventions and the Best Practices for Scientific Computing. Each module is fully documented and doctested. Before each new release, we make sure that all examples are working. As the ReScience Journal says: “Reproducible science is good. Replicated Science is better”.

### Future inclusion into Sage¶

Some modules may have a wider interest to the SageMath community (tikz_picture.py for example) and could be included in SageMath at some point. Please contact the author if you want to act as a reviewer for some module(s) and I will create a ticket on trac for its inclusion into SageMath.

### Release history¶

Version 0.5.1 (May 30, 2019)
Few fixes for the publication of “Induction of $$Z^2$$-actions on partitions of the 2-torus”. Improved html documentation.
Version 0.5 (April 10, 2019)
Few fixes for the version 2 of “Substitutive structure of Jeandel-Rao aperiodic tilings”. New additions includes solving Wang tilings problem using SAT solvers and a class for Polyhedron exchange transformations.
Version 0.4.4 (September 28, 2018)
Make import slabbe work in Sage with Python 3.
Version 0.4.3 (August 22, 2018)
Few fixes for the publication of “Substitutive structure of Jeandel-Rao aperiodic tilings”.
Version 0.4.2 (July 20, 2018)
Few fixes for the version 2 of “A self-similar aperiodic set of 19 Wang tiles”.
Version 0.4.1 (February 9, 2018)
Few fixes for the publication of “A self-similar aperiodic set of 19 Wang tiles”. New module to solve the Magic hexagon problem.
Version 0.4 (January 20, 2018)
Version 0.4 includes new modules for Wang tilings, 2d substitutions, polyhedron partitions, partial injections, ostrowski numeration and many improvements to other modules.
Version 0.3b2 (December 11, 2016)
Version 0.3b2 includes a new module for diophantine approximations, random point generation inside polytopes, analyzing sage building time, and many improvements to previous modules.
Version 0.3b1 (June 12, 2016)
Version 0.3b1 is now a Python package available in the Python Package Index (PyPI). It was migrated from the previous sage optional spkg old-style format. It also adds code to deal with bispecial factors, some new methods of graphs, substitutions and matrices.
Version 0.2 (November 25, 2015)
slabbe-0.2.spkg (documentation) provides modules on multidimensional continued fraction algorithms, matrix cocycles, languages and tikzpictures.
Version 0.1.1 (June 3, 2015)
slabbe-0.1.1.spkg fixes a bug with gcd import error.
Version 0.1 (August 27, 2014)
slabbe-0.1.spkg (documentation) contains modules on digital geometry, combinatorics on words and more.

## Module documentation¶

This reference manual contains many examples that illustrate the usage of the slabbe package. The examples are all tested at each release and should produce exactly the same output as in this manual.