Hello,
       I would like to discuss the implementation of Braid Groups. This 
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. 

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