Liverpool University Knot Theory Group
Programs and Procedures

Copies of the following programs and procedures can be downloaded for compilation on your own machine.
Some basic descriptions and instructions are attached.
Queries can be sent by e-mail to

This list can be found at URL or by following links from

See also the list of publications of the Liverpool Knot Theory group, where PostScript copies of some recent preprints can be found.

There are at present four programs, each calculating some invariant from a closed braid presentation. In each case the major constraint is the number of braid strings; the growth of calculation time with the number of crossings is roughly quadratic, and so typically it is not difficult to deal with braids having about 100 crossings.

Three of the programs are in Pascal. In each case the input required is the braid in terms of standard generators, with no separators, for example 123-2-231.

The three programs are

The three Pascal files need to be compiled before use. Via unix this might simply need the instruction
pc -o homfly br9z.pas to compile the first program (assuming it is in your files as br9z.pas) and to save the compiled version as an executable file called homfly.
Most recently (2021) I have used the Free Pascal compiler with Lazarus, to compile the first two programs on MacOSX, in both the 32bit and 64bit systems.
In the case of program 3, you may need to include the option -casesense in the compilation instructions, as there are both upper and lower case variable names used in it.

The last of the programs is a Maple procedure


Dept. of Mathematical Sciences
University of Liverpool
Peach Street