Hello,
I have gone through [1] and [2] for the implementation of Seifert
Matrix. [1] is the pdf containing the algorithm and [2] is the website
which has the same kind of implementation. I have created a gist [3] and
would be sending in a pull request sooner when I am done with refinements.
[3] calculates only the Seifert Matrix but this could be extended to get
the genus and Alexander's polynomial (If I am not wrong this can be done
from burau representation but from my understanding there are some issues
with generalizing)the braid word which is the input to the program [ [1]
has the explanation for the implementation of the above mentioned topics].
I would also like to mention that I would start working on the Vogel's
algorithm sooner after everything with [3] is done. Recently I came across
[4] which gives an alternate way of producing the knot diagrams (I still
have not tried it out on sage but I guess the material there would work
out). I would like to start working on my proposal for SoC and would
require help from the community on commenting and refining the ideas. I
would also like to know if 2 projects on the same topic would be accepted
as there seems to lot of work going onto preparing a graphical version of
knots. I request the mentors to look through the attached files.
[1] http://www.maths.ed.ac.uk/~s0681349/SeifertMatrix/SeifertMatrix.pdf
[2] http://www.maths.ed.ac.uk/~s0681349/SeifertMatrix/#braidnotation
[3] https://gist.github.com/amitjamadagni/9420632 [This is in very initial
stage, lots of work has to be done on it]
[4] http://www.mi.sanu.ac.rs/vismath/taylor2009/index.html
Amit.
On Wed, Mar 5, 2014 at 2:05 AM, Amit Jamadagni <[email protected]>wrote:
> Hello,
> As I mentioned I have started with the implementation but stuck mid
> way, Knotscape is using tables if I am not wrong and so is KnotAtlas but
> there has been no reference to any algorithms. And coming to the
> implementation of fox derivatives we cant expect the user to give me a
> large word if its a huge knot. It would be of great help if some reference
> to the algorithmic implementation is provided. I have searched through web
> to the best of my efforts for implementation through gauss codes, vogel's
> algorithm but there seems to be no computer algebraic to it. Thanks.
>
>
> On Sun, Mar 2, 2014 at 3:30 PM, Miguel Angel Marco <
> [email protected]> wrote:
>
>> Just a comment, i don't have the abilities to be a mentor of a javascript
>> editor. But i guess we could find someone that can.
>>
>> El domingo, 2 de marzo de 2014 08:56:35 UTC+1, Amit Jamadagni escribió:
>>>
>>> Hello,
>>> I had started with a sample implementation of braid word to DTcode and I
>>> had to take a break from it as my semester terminal exams started and would
>>> be working on after I am done with it which would be 2 days from now.
>>> Coming to the proposal I still have to figure out with more accuracy the
>>> things that could be implemented, even though I guess I have the main idea
>>> I need to structure it with the right algorithms and implementation
>>> details. So if once that is done then it would be give me a more clear idea
>>> of what could compliment each others work to bring the editor to life (In
>>> sense we start working on the constructing the base of two different things
>>> and at the end use each others work to complete the project) . Hoping to
>>> discuss this as soon as I am done with the terminal exams. Thanks.
>>>
>>>
>>> On Sun, Mar 2, 2014 at 10:47 AM, <[email protected]> wrote:
>>>
>>>> Yeah, persistent homology would be a separate issue. I can understand
>>>> if you don't want to take on a second project! It looks like Amit here is
>>>> already pretty deep into the implementation for knots, so maybe the editor
>>>> is better. Unless you don't mind collaborating on both, Amit?
>>>>
>>>> We should start figuring out the schedule/tasks part of the proposal.
>>>>
>>>> On Thursday, February 27, 2014 5:07:07 AM UTC-5, Miguel Angel Marco
>>>> wrote:
>>>>>
>>>>> Welcome,
>>>>>
>>>>> i am very happy that you have interest in participating in this
>>>>> project. From what i know, persistent homology does not fit really in the
>>>>> knot theory work (even though it would also be a nice addition). I agree
>>>>> with you that one of the first things we should do is to clarify which
>>>>> external software can be used, to wrap it instead of rewriting. Although,
>>>>> it might be tricky, some of this software is not maintained anymore, or
>>>>> has
>>>>> some limitations. So it could be the case that, even if there exists some
>>>>> external software to do the job, rewriting it in sage/cython would be a
>>>>> better option. That's why a part of the work should be to go through this
>>>>> available software and check how well it would fit for our purposes.
>>>>>
>>>>> If you feel that writing the knot/link class is not enough work, i
>>>>> would also suggest to write an interactive knot editor (following the idea
>>>>> of the graph editor, although, if possible, i would really like something
>>>>> like the knotplot editor) for the notebook. I really don't know much about
>>>>> javascript, so i cannot tell how much work it would take. Anyways, it
>>>>> could
>>>>> perfectly be a separate project.
>>>>>
>>>>> If you have any further questions, please ask.
>>>>>
>>>>> El jueves, 27 de febrero de 2014 03:44:41 UTC+1,
>>>>> [email protected]ó:
>>>>>>
>>>>>> Just saw the GSOC announcement - awesome stuff!
>>>>>>
>>>>>> My name is Andrew Silver, I'm an undergraduate mathematics major at
>>>>>> the University of Florida (Gainseville, FL).
>>>>>> I currently do numerical/statistical work in computer vision: I'm
>>>>>> comfortable in C++, familiar with Java, HTML5, Javascript, and recently
>>>>>> Sage/Python.
>>>>>>
>>>>>> This semester I was lucky enough to get into a graduate course in
>>>>>> Computational Topology (Topological Data Analysis), and I'm hooked.
>>>>>>
>>>>>> Why Sage? I compiled Sage as soon as my prof gave us a long hw
>>>>>> assignment that involved computing homology of a torus, klein bottle, and
>>>>>> the Real Projective Plane...
>>>>>> ..based on triangulations that had 27x18 boundary matrices we had to
>>>>>> get in smith form... (I actually found a bug in matrices mod 2 that I
>>>>>> have
>>>>>> a ticket open for, just got to write up some doctests and it should be
>>>>>> fixed). I used Sage instead of Matlab because I couldn't figure out how
>>>>>> to
>>>>>> get Matlab to save the u,v matrices - open source is the way to go.
>>>>>>
>>>>>> What do I want to do? I'd love to work on implementing knots/links as
>>>>>> per ( https://docs.google.com/document/d/15v7lXZR1U4H2pT21d2fyPduY
>>>>>> Gb74JAFjkXJ6CWYmYfw/pub#h.6l9ekqoc9br7 ), writing classes,
>>>>>> functions, invariants, etc. A potential caveat is how much we want to
>>>>>> "reinvent the wheel" because there are already existing implementations
>>>>>> in
>>>>>> other packages for some of these things.
>>>>>>
>>>>>> If there isn't enough work there, I'd also be interested in
>>>>>> integrating Stanford's computational topology tools into Sage (
>>>>>> http://comptop.stanford.edu/programs/) for persistent homology
>>>>>> calculations. Dr. Carlsson (Stanford) gave a talk at UF this week and
>>>>>> told
>>>>>> me that the tools are still under development, so it would probably be a
>>>>>> matter of getting permission if the community wants to go this route. Or
>>>>>> we
>>>>>> could start from scratch. I'm thinking Persistence Diagrams, Barcodes,
>>>>>> witness complexes, etc.
>>>>>>
>>>>>> Other math exposure:
>>>>>> Linear Algebra
>>>>>> Introductory Probability
>>>>>> Calc I - III
>>>>>> Discrete Mathematics
>>>>>>
>>>>>> Why do I want to do this?
>>>>>> If I don't contribute to Sage, I'd be implementing algorithms for my
>>>>>> research anyway. Might as well share them with other people!
>>>>>>
>>>>>> github that I contribute to when I have time: https://github.com.
>>>>>> You can reach me by email at [email protected]
>>>>>>
>>>>>>
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>>>
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