Can this be a feasible idea to be worked upon for SoC ?? Any comments would be great.
On Thu, Jan 30, 2014 at 7:54 PM, Amit Jamadagni <[email protected]>wrote: > I have gone through the package and it seems to have integrated sage and > SnapPy for computing Alexander's polynomial. They have used the idea of > manifolds to implement (I would like to mention that my grasp of subject is > not that far even though I understand the basics of manifold as a local > homeomorphism to real line( I might be completely wrong)). My plan was to > start with implementing the Braid groups with the braid word, assigning > numbers to the generators and reading from top to bottom which has been the > most used algorithm to construct braids. Then I would like to use the > concept of Braid words to get to the Alexander's polynomial (That could be > achieved through Burau representation). Then other representation like > Lawerence - Krammer could be achieved by relating to matrices (The points I > have mentioned above have been already been implemented in various other > modules). I had the idea of implementing the Kaufmann's invariant alteast > for small number of crossings by the following way : As we can construct a > knot from a braid, if the crossing at each point can be mentioned by X for > one going over the other and X inverse for the one going below the other > and then applying the conditions and splitting it for each crossing and > representing the new replacements by one and the other by zero could lead > to the final polynomial.I am even trying to understand the implementation > of invariants like the HOMFLY - PT polynomial and Khovanov Homology > (atleast the arc representation is possible to implement). My initial > attempt was to relate the braids to anyon braiding which act as gates to > perform quantum computation (I could not find any material regarding this > but I am still on the search).My recent realization being it can be > achieved as a solution to Yang Baxter Equations. These are the ideas I have > had but the algorithms relating to the implementation still needs heavy > thinking. > > > On Thu, Jan 30, 2014 at 4:23 AM, David Joyner <[email protected]> wrote: > >> On Wed, Jan 29, 2014 at 4:32 PM, Amit <[email protected]> wrote: >> > Hello, >> > I would like to discuss the implementation of Braid Groups. This >> >> Are you planning on going beyond what is already known? >> http://www.math.uiuc.edu/~nmd/snappea/ >> If so, what is your plan? >> >> > would involve the implementation of various invariants related to Braids >> > like the Alexander's polynomial >> > (http://mathworld.wolfram.com/AlexanderPolynomial.html) by building up >> the >> > Burau representation of the same >> > (http://mathworld.wolfram.com/BurauRepresentation.html) [There are more >> > accurate versions of Braid Group representation] and various other >> > properties relating to permutation group underlying Braids. However I >> could >> > not think of any idea which would implement the other invariants like >> the >> > Kauffman's invariant for knots (I wonder whether such kind of >> implementation >> > can be worked around atleast for knots with less number of crossings). >> I was >> > also looking through the implementation of Braid Diagrams by various >> means >> > one attempt was by using TikZ. Braid Diagrams can be converted into link >> > diagrams as every link can be represented as closed Braid. The main >> > motivation behind everything is to implement certain features in Knot >> Theory >> > module of Mathematica >> > ( >> http://katlas.math.toronto.edu/wiki/The_Mathematica_Package_KnotTheory%60 >> ) >> > in Sympy. Thanks. >> > >> > -- >> > You received this message because you are subscribed to the Google >> Groups >> > "sympy" 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/sympy. >> > For more options, visit https://groups.google.com/groups/opt_out. >> >> -- >> You received this message because you are subscribed to the Google Groups >> "sympy" 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/sympy. >> For more options, visit https://groups.google.com/groups/opt_out. >> > > -- You received this message because you are subscribed to the Google Groups "sympy" 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/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CAHmaejw%3DFsTVmeKc1%2Bcfu1HYH%2ByGzjSx%2By5%3D1qsmWwHM4%3DadsA%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
