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Assume I have a polygonal knot, $K$, represented as its set of vertices $\{\mathbb{v}_i| \mathbb{v}_i\in\mathbb{R}^3\}_{i=1,...,n+1}$, where $n$ is significant, let's say $100<n<500$.

Which software packages exist that will take this specification of the knot (just the list of vectors, not a PD code or anything like that), and compute finite type invariants of $K$?

I'm in particular interested in the second Vassiliev invariant, but curious about others too. The only option i've come across thus far is pyknotid, though I would be curious to learn about others too.

Thanks in advance!

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    $\begingroup$ Check out [ reference.wolfram.com/language/ref/KnotData.html ] though it might have limitations on $n$ values. $\endgroup$
    – Prem
    Commented Apr 11 at 2:40
  • $\begingroup$ Thank you @Prem ! I had come across this before actually, and would like to use it...however it's not clear to me how to instantiate the Knot instance in KnotData just given the list of vertices. It seems that one needs to pass a generic name like "trefoil" or "figure eight". Do you know how to use KnotData to create knots using just the list of vertices? Appreciate any help $\endgroup$
    – guest
    Commented Apr 12 at 12:27
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    $\begingroup$ Oh , unfortunately I have almost no idea about using KnotData within Wolfram tool. You will have to use the Documentation with Examples to know more. Even then , it might not allow 100-500 edges ! $\endgroup$
    – Prem
    Commented Apr 16 at 6:31

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