The Sage worksheet delta-one-via-gröbner-basis.sws allows you to input a knot and calculate \(\delta_1\) of that knot. See my paper for a definition of \(\delta_1\) and a description of the algorithm. To get this worksheet to run, you need to download
Go ahead and install Sage.
Before you install Macaulay2, please read this entire paragraph. I ran into a problem here using Mac OS 10.8. Macaulay2 has an installation procedure that didn’t play nice with my Sage installation. The rest of the paragraph is dedicated to my solution. From a completely Macaulay2 free state (I had to remove some configuration files created by the Macaulay2 installer), I downloaded Macaulay2 and stored the folder in /Applications. In the terminal, I created a symbolic link in /usr/bin/ to the Macaulay2 executible (M2) via the command ‘sudo ln -s /Applications/Macaulay2-1.4/bin/M2 /usr/bin/M2’. Your /path/to/M2 might be slightly different depending on where you put the Macaulay2 folder and what version you downloaded. Now at this point the terminal command ‘M2’ runs Macaulay2, and Macaulay2 works inside of the Sage notebook interface.
To check that Sage and Macaulay2 are compatible, execute the command ‘macaulay2(‘2+3′)’ in the Sage notebook. If it returns 5, then things are probably working. If there is an error message, I might be able to help but will probably send you to the Sage or Macaulay2 Google Group pages.
Once Macaulay2 is working inside Sage, upload the delta-one-via-gröbner-basis.sws worksheet into the Sage notebook interface. There you can see some examples of a \(\delta_1\) calculation and learn how to compute \(\delta_1\) for any examples you wish.