Alexander polynomial can be computed directly from the braid expression. It would also be good to have different methods to compute the invariants from dofferent representations.
El jueves, 27 de febrero de 2014 19:12:39 UTC+1, Amit Jamadagni escribió: > > Yes, I was thinking of converting the braid words to DT codes and then > once this is achieved we can get the Alexander's polynomial (this was > achieved in knotaltas) and I guess if one of the invariants is obtained > converting them into others might not be a heavy task(I am not completely > sure of the algorithms though but I guess this can be achieved). I have > gone through knotscape (not completely though) and have started working on > converting given braid word representation into DT codes for a start. > > > On Thu, Feb 27, 2014 at 11:31 PM, Miguel Angel Marco > <[email protected]<javascript:> > > wrote: > >> Maybe making a c library out of knotscape, interfacing it and wrap it in >> a class would be a good way to approach this project. But then again, there >> are more software available for similar tasks. Comparing and choosing the >> best option could also be interesting. >> >>> >>> IMHO a good and timely project would be knot recognition, a la >>> knotscape. It seems that the only present alternatives to knotscape >>> are Mathematica packages. Knotscape also computes polynomial invariants, >>> so this >>> would be a nice feature to get them properly as polynomials rather >>> than as lists of coefficients... >>> >>> Incorporating parts of knotscape into Sage looks doable, as this is >>> plain C code. True that it is old, but this does not make it less >>> viable. >>> >>> Dima >>> >>> >>> >>> >>> > >>> > 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/15v7lXZR1U4H2pT21d2fyPduYGb74J >>> AFjkXJ6CWYmYfw/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] <javascript:> >>> >> >>> >> >>> >> >>> > >>> >>> -- >> 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] <javascript:>. >> To post to this group, send email to [email protected]<javascript:> >> . >> 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. 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