Edits, dowker notation, HOMFLY …

Hello everyone,
This week we have been working on editing the code to reach the standards along side running the tests. A decent amount of time has been spent on documentation. Plot methods and 3d co ordinates seem to be taking a longer time and even Miguel is giving this a good thought, so as of now these remain still in the thinking phase. In the meantime Miguel has shared some great work regarding the implementation of HOMFLY polynomial, stronger invariant to distinguish links. I am enjoying myself going through it as it shows how it is related to few other things which are of interest to me. Here is the link for it

http://www.maths.dur.ac.uk/Ug/projects/highlights/PR4/Goulding_Knot_Theory_report.pdf

So as a part of it I have implemented the dowker notation which is nothing but the (Ux, Ox) that is under-cross, over-cross at a particular crossing. This was a straight forward implementation as we had everything already present the PD code and the orientation of the crossings. In addition to this we have been working on the code to make it better and more cleaner. We have dropped the support to take in key words, now it is just that we directly give in the input for the link (the user need not mention whether it is a braid, PD_Code, or oriented gauss code) we have made it possible to detect from the way the user inputs what kind of input it is. There are few minor issues with code refactoring which we have been working on. Here is the link for the latest code :

https://github.com/amitjamadagni/sage/blob/week14/src/sage/knots/link.py

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