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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