Hello,
Thanks for the reply. It would be helpful if you could post your
thoughts on the implementation [3] (I know its in the rudimentary level but
I would like to start off there, is there a better way of getting around or
it is fine to go on enhancing the current implementation. And it would be
valuable if some thoughts were posted on [4]. I have started to draft the
proposal, once it gets into a presentable stage I would like your comments
on it.
Amit.
On Sat, Mar 8, 2014 at 3:44 PM, Miguel Angel Marco <[email protected]
> wrote:
> I guess it would be possible to have two different students, one working
> in the backend and another one in the javascript editor. Bat that would
> deppend on several things: the number of students that google decides to
> fund for the sage organization, the quality of the proposals, tha
> availability of mentors...
>
> I would be happy to answer your questions about your proposal. Just ask.
>
> El viernes, 7 de marzo de 2014 22:50:02 UTC+1, Amit Jamadagni escribió:
>>
>> 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/
>>>>>>>> 15v7lXZR1U4H2pT21d2fyPduYGb74JAFjkXJ6CWYmYfw/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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>>>
>>>
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