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I would like to understand how a computer program for computing Khovanov homology works. The particular program I have in mind is by John Baldwin: https://web.math.princeton.edu/~baldwinj/Kh.cpp The main point I don't understand is how one encodes each resolution of a knot diagram (which can be complicated with nested circles, etc.) and also how one computes the number of components of such a resolution.

There are other similar programs by Bar-Natan or Cotton Seed but they are more comprehensive (and so more difficult to peruse).

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    $\begingroup$ You may want to mention this documentation page in your question: www2.bc.edu/john-baldwin/trans.html. It explains some things about the input format that don't seem to be mentioned in the source code comments, and it could be quite valuable for people trying to answer your question. $\endgroup$
    – Vectornaut
    Commented Aug 31, 2014 at 10:08
  • $\begingroup$ I think your question is "how to use it", not "how it works" (in the sense of, what algorithm does it use); either way, you might make this clearer. $\endgroup$
    – Allen Knutson
    Commented Aug 31, 2014 at 11:39
  • $\begingroup$ Vectornaut: That page describes the input which is a braid word. @Allen Knutson No it isn't. $\endgroup$
    – Reza Rezazadegan
    Commented Aug 31, 2014 at 13:50
  • $\begingroup$ Weird, I don't know why I was insisting on reading it the other way. $\endgroup$
    – Allen Knutson
    Commented Aug 31, 2014 at 22:42

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