This project is designed to find the average shape of a Legendrian Knot. It does so in the following way:
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Given an integer n, generate n random points. If it is a valid point, add it to the knot, else generate a new point.
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Once the knot is generated, create an array of all of the crossings in Ewing/Millett notation.
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Use this array to calculate the HOMFLY polynomial to classify the knot.
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Repeat some large number of times, keeping track of the knot classification.
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Output the percentage of each knot created
To use on a Linux machine:
make./run- follow the prompts
Note that it will create multiple files for manual inspection/analysis - the final counts/percents will be in finalResults files and those including Bennequin will be in finalResultsBR files.
TODO:
- clean up generateNotation in func.cpp
- change checkSameLine in func.cpp to be KnotVertex rather than knotNot based
- change checkIfV in func.cpp to be KnotVertex rather than knotNot based
Working:
- Knot-Generation
- Crossing Generation
- Crossing Labelling
- Notation Generation (?)
- Passing File to Homfly code
- parse homfly output
- compute percentage of each knot created
- add B/R notation/parsing
- add knot generation by crossing
Notation Generation:
- No-crossing knots
- One-crossing knots
- Unknots of most crossings
- Seems to be working - haven't run into any errors in quite a while
/****
Sources:
http://stackoverflow.com/questions/9878965/c-rand-between-0-and-1
http://www.cplusplus.com/forum/beginner/49408/ (Disch's answer)
http://stackoverflow.com/questions/14176776/find-out-if-2-lines-intersect
http://www.codeproject.com/Tips/862988/Find-the-intersection-point-of-two-line-segments
http://stackoverflow.com/questions/563198/how-do-you-detect-where-two-line-segments-intersect
http://stackoverflow.com/questions/20010909/how-to-loop-through-multiple-functions-in-c
https://www.codeproject.com/Articles/7150/Member-Function-Pointers-and-the-Fastest-Possible
http://www.cplusplus.com/forum/beginner/27582/
http://stackoverflow.com/questions/1560492/how-to-tell-whether-a-point-is-to-the-right-or-left-side-of-a-line
https://msdn.microsoft.com/en-us/library/7k66t42c.aspx
http://stackoverflow.com/questions/4316442/stdofstream-check-if-file-exists-before-writing
http://stackoverflow.com/questions/191757/how-to-concatenate-a-stdstring-and-an-int
http://stackoverflow.com/questions/14070940/c-printing-out-map-values
http://stackoverflow.com/questions/5056645/sorting-stdmap-using-value
http://stackoverflow.com/questions/2896600/how-to-replace-all-occurrences-of-a-character-in-string
*****/
This project was done as a math research project under the advisement of Professor Lisa Traynor of Bryn Mawr College's Department of Mathematics and Ph.D. candidate Samantha Pezzimenti.
Special thanks to Charles and Harold for letting me talk at them about this and acting as sounding boards