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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