foam-gl1

foam-gl1 is a computer program which calculates the symmetric gl1-homology of links, introduced in [RW]. The program is written in python3 and uses the libraries NumPy and PyTorch. It takes as input a braid representative of a link, expressed either as a sequence of integers or as a word made up of uppercase (positive crossings) and lowercase (negative crossings) letters. A typical use is:

> python3 foam-gl1.py AbAb

In this line, AbAb represents the braid σ1σ−2σ1σ−2 and the program computes the (non-equivariant) symmetric gl1-homology of its closure, that is the figure-eight knot. 

More specifically, foam-gl1 computes the following:

• The non-equivariant symmetric gl1-homology of an uncolored link (to show the matrices of the differential, add  -m   between the name of the program and the braid)

• The symmetric gl1-homology in characteristic p (prime) of a braid diagram. To compute in char 3, for instance,  add  -p 3   between the name of the program and the braid. In order to compute in characteristic p, the software SpaSM must be installed.

A description of the program and the algorithm underlying it is given here.

foam-gl1 is available for download here.