Thanks for the reply. The matrix b is Seifert Matrix but there has to be lot of simplification as the the answer does not match for all the cases. I am still to get acquainted with Sage matrix methods, so instead I got the rows and initialized every element to zero and then started to manipulate the matrix as per the homology generators algorithm given in the pdf that I attached. I would refine this further and post it back . Thanks for the review.
On Sat, Mar 8, 2014 at 9:16 PM, Miguel Angel Marco <[email protected] > wrote: > 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]>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] escribió: >>>>>>>>>> >>>>>>>>>> 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] >>>>>>>>>> >>>>>>>>>> >>>>>>>>>> -- >>>>>>>> You received this message because you are subscribed to the Google >>>>>>>> Groups "sage-gsoc" group. >>>>>>>> To unsubscribe from this group and stop receiving emails from it, >>>>>>>> send an email to [email protected]. >>>>>>>> To post to this group, send email to [email protected]. >>>>>>>> >>>>>>>> Visit this group at http://groups.google.com/group/sage-gsoc. >>>>>>>> For more options, visit https://groups.google.com/groups/opt_out. >>>>>>>> >>>>>>> >>>>>>> -- >>>>>> You received this message because you are subscribed to the Google >>>>>> Groups "sage-gsoc" group. >>>>>> To unsubscribe from this group and stop receiving emails from it, >>>>>> send an email to [email protected]. >>>>>> To post to this group, send email to [email protected]. >>>>>> Visit this group at http://groups.google.com/group/sage-gsoc. >>>>>> For more options, visit https://groups.google.com/groups/opt_out. >>>>>> >>>>> >>>>> >>>> -- >>> You received this message because you are subscribed to the Google >>> Groups "sage-gsoc" group. >>> To unsubscribe from this group and stop receiving emails from it, send >>> an email to [email protected]. >>> To post to this group, send email to [email protected]. >>> Visit this group at http://groups.google.com/group/sage-gsoc. >>> For more options, visit https://groups.google.com/d/optout. >>> >> >> -- > You received this message because you are subscribed to the Google Groups > "sage-gsoc" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/sage-gsoc. > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "sage-gsoc" group. 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