Has anyone ever written code for computing Khovanov homology in Macaulay2 or other similar software? I know there are various excellent programs for computing Khovanov homology, but I'm currently interested in a variant that probably will require the algebraic capabilities of Macaulay2 - in particular, the ability to work with modules over a polynomial ring with multiple variables. I'm curious to know if anyone has ever done this before to avoid reinventing the wheel.
$\begingroup$
$\endgroup$
1
-
2$\begingroup$ I'd ask Ben Webster who in grad school had a program I'm pretty sure was in Macaulay for triply graded HOMFLY homology after Khovanov's Soergel bimodule paper came out. My recollection was that Macaulay2 was actually missing some key features and so he'd done it in Macaulay(1), but I could be misremembering. $\endgroup$– Noah SnyderCommented Sep 20, 2019 at 14:59
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
Adam, I'm not sure if you still need this but Sage has a program to compute the Khovanov homology of a link and has an interface with Macaulay 2/uses Macaulay 2.
As a disclaimer, I am not an expert on how the SAGE program to compute Khovanov homology works. In particular, I'm not sure if it uses a divide and simplify approach like Bar Natan's programs or a much slower approach of computing the entire cube of resolutions.
https://doc.sagemath.org/html/en/reference/knots/sage/knots/link.html
https://doc.sagemath.org/html/en/reference/interfaces/sage/interfaces/macaulay2.html
