Hello,
I am Amit, a 3rd year undergraduate pursuing Masters in Mathematics
along with B.E in Electronics and Electrical. I have already posted about
my interest to participate in GSoC 2014 by contributing to Matroid Theory
but then I did not see Knot Theory in the Ideas list. I was excited to
participate so that made me choose a topic which was more closer to
Mathematics and at that time it(Matroid Theory) was the only one I saw.
Coming back, I want to work on this as I am more familiar with this theory
and have done some relevant course work (I have done a semester long course
in Algebra, Topology and currently doing Algebra II). I was introduced to
the theory of knots as I started to understand the theory of quantum
computation by braiding. When I started to dig deeper into the subject I
found algorithms were being developed in the quantum world to find the
various invariants of knots like the Kauffman invariant, Jones Polynomial,
the HOMFLY invariant which would be faster in this realm compared to the
classical world. In the attempt to understand the theory I started with
Braid groups by Kassel (to understand the theory). I have seen the source
of sage and it has a library for Braid groups. As every link can be
represented as closed braid I guess we can start to extend this library to
the represent Links and Knots using TikZ (however this is a very rough
idea).We could then move onto implement the various invariants (This is
just an idea I still have to ponder upon the general feasibility). In my
attempt to learn the what has been implemented generally in Knot theory I
have referred to the following link (
http://katlas.org/wiki/The_Mathematica_Package_KnotTheory%60 ). Coming to
my coding experience I have decent knowledge in python and I have made an
attempt in contributing to Sage by trying to fix ticket #15003. In addition
to this I have worked on successfully fixing patches in other open source
software. I am really excited and looking forward to work on this and I
would like the mentors to throw some light on what could be implemented to
make it a package with decent capabilities. Thanks.
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