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Knot Theory and Sage?

asked 2011-08-02 09:24:37 -0500

StevenPollack gravatar image

updated 2015-01-13 11:21:02 -0500

FrédéricC gravatar image

I was wondering what kind of Knot Theory tools Sage has? I've done a couple google searches, as well as a doc search in the Sage reference manual; everything's turned up bunk.

Does anyone know of any Knot Theory tools in sage? In particular, knot tables?

Thanks,

Steven

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answered 2011-08-02 14:26:44 -0500

kcrisman gravatar image

updated 2016-06-15 15:08:49 -0500

Edit: Knots are now in Sage!!!

Old answer: As far as I know, there is not any knot theory in Sage, though there is lots of combinatorics and some algebraic topology.

The most natural thing to do would be to port the Knot atlas somehow, and (if one was very bold, and had permission) the Mathematica package that creates it. I have had people ask about this before, and it's a very natural thing to do in Sage. If you know the people in charge of this project, you should see whether they are open to this (if only for having two implementations of the same algorithm to check for bugs).

Update: Braid groups have now been in Sage for a while, including plotting.

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As an interesting note, some of it uses Python: http://katlas.org/wiki/Heegaard_Floer_Knot_Homology

Mike Hansen gravatar imageMike Hansen ( 2011-08-02 14:38:02 -0500 )edit

I've checked out the Knot Atlas, but the fact that I needed to use mathematica to harness their software kept me from seriously considering anything over there. I'm surprised that no one has tried contacting the Knot Atlas people regarding a Sage port. As far as I know the two admin's are U of Toronto professors, right? So they shouldn't be that opposed to an open-source frame-work to their project... Thanks for the reply, by the way.

StevenPollack gravatar imageStevenPollack ( 2011-08-03 11:52:12 -0500 )edit

And I've spoken with at least one person who thinks they would be fairly open to it. Of course, it would be a big project to convert all that code to Sage, I would think. ?

kcrisman gravatar imagekcrisman ( 2011-08-03 16:47:58 -0500 )edit
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answered 2014-08-25 14:47:35 -0500

mmarco gravatar image

Amit Jamadagni has been working on a knot theory module in this year's GSoC program, under my mentoring. The result is a Link class with some basic functionality (mainly conversion between different representations of a link, and computation of some invariants). It still needs polishing, but i expect we can have something ready to be merged in sage in the following weeks.

From that, there would still be a lot of work to do to improve it, but the basic infrastructure would be there.

https://www.google-melange.com/gsoc/p...

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Oh, this is really great news! Just a few weeks ago several people at http://wiki.sagemath.org/days60 were really interested in knowing what happened with that project - we didn't hear much about it on the list :)

kcrisman gravatar imagekcrisman ( 2014-08-26 13:58:50 -0500 )edit
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answered 2011-08-03 10:30:54 -0500

Simon King gravatar image

A long time ago, I created a Wiki with the purpose to collect (algebraic) topology software that could eventually become part of Sage (as an optional package, at least).

The wiki is here. However, it seems that nothing came out of it.

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For what it's worth, that wiki page was one of the first places I learned about Sage (from some google search), and I still think about it from time to time . . .

niles gravatar imageniles ( 2014-08-27 13:32:45 -0500 )edit
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answered 2013-04-19 03:48:42 -0500

turion gravatar image

Would it be a good start to implement the braid category for sage? Then it might be easy enough to port the knot atlas. All link diagrams (and therefore, knot diagrams) are morphisms in the braid category, from the empty object to itself. And after that, maybe define the category of braided monoidal categories? Then a lot of knot invariants are accessible as functors.

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I think implementing anything along these lines would be a good idea.

John Palmieri gravatar imageJohn Palmieri ( 2013-04-19 06:53:33 -0500 )edit

Update: Braid Groups are now in Sage - http://trac.sagemath.org/ticket/12339 - including plotting.

kcrisman gravatar imagekcrisman ( 2014-08-14 03:45:21 -0500 )edit

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Asked: 2011-08-02 09:24:37 -0500

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Last updated: Jun 15 '16