HTML
version with output
These pages contain programs and files used to calculate quandle cocycle knot invariants for various cases. The data files are either text files (*.txt) or maple input files (*.m). The Maple worksheets were created with Maple 8.
This first knot file contains the braid words for the prime knots from Rolfson's table of knots. Only knots with 8 and fewer crossings are included in this file. This file is a text file that can be read into a Maple worksheet. The knots are stored in an array that has the name "bw". There are 35 knots that satisfy the above condition. These knots are then ordered as they arrear in the table. Therefore, bw[1] is the trefoil, bw[2] is the figure eight knot and so on. This file is used in sample worksheets for the untwisted case and the twisted case.
knot_tableThis is another textfile, knotsLivingston.txt, containing information for the knots formatted to be read into a Maple worksheet. The data was generated form Charles Livingston's knotinfo database and then reformatted. This file contains the knots in the table up to and including 12 crossings. The information is stored in an array named "Knot". "Knot" is a two dimensional array, Knot[i][j]. The non-negative integer i represents the knot that you want to access and ranges from 0 to 2976. The second term, j, has a value in {1,2,3}. A value of j=1 will give the knot name, j=2 will give the braid word, and the value j=3 will return the Alexander polynomial of the knot. For example, the trefoil information is stored as, Knot[0,1]:= "3_1";Knot[0,2]:= [1,1,1];Knot[0,3]:= t^2-t+1;. This file is used in WorksheetIII for the Mochizuki Polynomial Cocycle Cases section.
knotsLivingstonThe next file is a text file containing quandles. It is formatted to be read into a Maple worksheet. These quandles were taken from [CKS00]. This file contains only the quandles that had non-trivial torsion part in one of its homology groups. The quandles are named by Qi_j where i represents the order of the quandle and j represents the jth quandle satisfying the above conditions as it appears in the book of the given order i ranging from 3 to 6. There were 25 quandles satisfying the condition for 6 element quandles so j ranges from 1 to 25 (eg. Q6_1, ... , Q6_25). These quandles are stored as its Cayley table in a two dimensional zero indexed array. Programs for generating special quandles not appearing in this file can be found in WorksheetIII in the Mochizuki Polynomial Cocycle Cases section. This file is used in sample worksheets for the untwisted case and the twisted case.
QuandlesThis worksheet explains Maple procedures that will calculate quandle two and three cocycle knot invariants for the untwisted case. The Maple worksheet was created with Maple 8. There is also an html version with outputs for those that do not use Maple.
Maple 8
worksheet cocysample.mws
This worksheet will require two data files, knot_table and quandle, and the Maple input file Knotpkg.m. The two data files are located at the beginning of this page.The Maple input file is just the code for the procedures saved into a special file. An HTML version of the code is also available for those who do not use Maple.
HTML
version of untwisted code
Maple procedures for untwisted case stored as a Maple input file necessary for cocysample.mws
Maple 8 worksheet
containing the code for the untwisted case
This worksheet explains Maple procedures that will calculate quandle two cocycle knot invariants for the twisted case. The Maple worksheet was created with Maple 8. There is also an html version with outputs for those that do not use Maple.
cocysampleTwisted.mws Maple 8 worksheet
This worksheet will require two data files, knot_table and quandle, and the Maple input file KnotpkgT.m. The two data files are located at the beginning of this page.The Maple input file is the code for the procedures saved into a special file. An HTML version of the code is also available for those who do not use Maple.
KnotpkgT.m Maple procedures for twisted case stored as a Maple input file necessary for cocysampleTwisted.mws
KnotpkgT.mws Maple 8 worksheet
containing the code for the twisted case
These files contain programs for calculating two and three cocycle polynomial invariants. There are procedures to generate finite Alexander quandles and the values for the Mochizuki polynomial cocycles.
Maple
8 sample worksheet cocysampleIII for Mochizuki polynomial case in HTML.
Maple
8 sample worksheet cocysampleIII.mws for Mochizuki polynomial case.
This worksheet requires the following Maple input files:
Maple input file PolycocInvpkg.m containing procedures for worksheet cocysampleIII.mws
Maple input file alexQuanpkg.m containing procedures to generate Alexander quandles for worksheet cocysampleIII.mws
The HTML and Maple worksheet versions:
HTML
version of PolycocInvpkg.mws
Maple
worksheet containing code for PolycocInvpkg.m
HTML
version of AlexQuandlepkgprocs
Maple
worksheet containing code for AlexQuandlepkgprocs
Worksheet IV and its packages are an update of the previous three worksheets. The added features and improvements include:
One consequence of these new features is that the programs become system dependent. These packages have only been implemented and tested on various distributions of Linux. A link to the source code of the C coloring program will be given to allow you access to the file if you need to compile it for your particular OS. Perhaps if time permits or demand is high, we could compile and implement it for your particular OS and symbolic computation software. The sample worksheet explains more about the use and how the new coloring method works. An html version is included below.
Maple
8 sample worksheet cocysampleIV.
Maple
8 sample worksheet samplewkstIVMaple8.mws.
This worksheet requires the following files:
Maple input file quancocDLLpkgmaple8.m containing procedures for worksheet samplewkstIVMaple8.mws.mws
Maple input file alexQuanpkg.m containing procedures to generate Alexander quandles.
shared object file (DLL) to be linked to Maple for coloring the braids.
Code for the procedures: