Patrick Dehornoy

Patrick Dehornoy

Programmes / Programs

Except the braid applet, the programs are primarily proposed as iOS executable binaries (running on any Mac with an intel chip), but, if you dont use a Mac, you can easily run them using the Docker software, which automatically produces the version that is relevant for your computer. To do it: Then, for running the program called XXX:

Acknowledgement: Many thanks to Antoine Petiteau for introducing me to the Docker technology and teaching me how to use it; this is a very convenient solution for making nonstandard languages usable.

MoKa ("monoid calculus")

This program implements various algorithms for working in a monoid defined by a complemented presentation, typically an Artin-Tits monoid. One can work with elements of the monoid, and with multifractions, which are sequences of elements of the monoid representing the elements of its enveloping group. The main tools are subword reversing and multifraction reduction as defined in arXiv 1606.08991, 1606.08995, 1606.09018, and 1701.06413.

Documentation (including instructions for saving in external files when using Docker):


This rudimentary program performs simple braid operations, in particular involving orders. The main comparison tool is handle reduction, which, starting with an arbitrary braid word, returns an equivalent sigma-definite word (the generator with lowest index does not appear both positively and negatively).


(with Jean Fromentin) Handle reduction of braids

This program demonstrates some aspects of the mathematical theory of braids. It allows the user to draw braid diagrams and to perform a few basic operations, namely ecognizing if a braid diagram is really braided or, more generally, if a braid diagram can be continuously deformed into another one.