I dont think the approach in [4] would be very helpful in our case. It is
not clear to me weather every knot can be representad that way, and even if
it can, determine the actual parametrization from the combinatorial data
contained in a diagram sounds like a really difficult problem. It would be
nice to have 3d representations of knots, but that is definitely not the
way to go.
About your code in 3, is hard for me to follow exactly what you are doing.
What is the matrix b supposed to be? There are also some things that could
be done simpler. For instance
new = []
for i in range(len(x)):
a = abs(x[i])
new.append(a)
Can be accomplished with
new=map(abs,x)
or
new=[i.abs() for i in x]
which are both simpler and easyer to read and maintain.
Or also, missing can be computed just as the difference of the set of
range(1,sorted[-1]+1) and sorted.
El sábado, 8 de marzo de 2014 11:24:05 UTC+1, Amit Jamadagni escribió:
>
> 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]<javascript:>
> > 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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