Hello,
I have gone through [1] and [2] for the implementation of Seifert
Matrix. [1] is the pdf containing the algorithm and [2] is the website
which has the same kind of implementation. I have created a gist [3] and
would be sending in a pull request sooner when I am done with refinements.
[3] calculates only the Seifert Matrix but this could be extended to get
the genus and Alexander's polynomial (If I am not wrong this can be done
from burau representation but from my understanding there are some issues
with generalizing)the braid word which is the input to the program [ [1]
has the explanation for the implementation of the above mentioned topics].
I would also like to mention that I would start working on the Vogel's
algorithm sooner after everything with [3] is done. Recently I came across
[4] which gives an alternate way of producing the knot diagrams (I still
have not tried it out on sage but I guess the material there would work
out). I would like to start working on my proposal for SoC and would
require help from the community on commenting and refining the ideas. I
would also like to know if 2 projects on the same topic would be accepted
as there seems to lot of work going onto preparing a graphical version of
knots. I request the mentors to look through the attached files.
[1] http://www.maths.ed.ac.uk/~s0681349/SeifertMatrix/SeifertMatrix.pdf
[2] http://www.maths.ed.ac.uk/~s0681349/SeifertMatrix/#braidnotation
[3] https://gist.github.com/amitjamadagni/9420632 [This is in very initial
stage, lots of work has to be done on it]
[4] http://www.mi.sanu.ac.rs/vismath/taylor2009/index.html
Amit.
On Tue, Feb 25, 2014 at 3:11 AM, Amit Jamadagni <[email protected]>wrote:
> 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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