This CDROM is part of Appendix B of the Ph.D. thesis "Seifert's Algorithm, Chatelet Bases and the Alexander Ideals of Classical Knots" 
by Killian Michael O'Brien. The CDROM contains the files

README
3cross.txt
4cross.txt
5cross.txt
6cross.txt
7cross.txt
8cross.txt
9cross.txt
10cross.txt
11cross.txt
12cross.txt
13cross.txt
14cross.txt
knots1-14.txt
Algorithms.mws
Process.mws

The .txt files contain Chatelet Bases for the Alexander ideals of prime knots of up to 14 crossings. It is intended that these files be read and 
used with the Maple worksheet Process.mws but they can also be browsed with any text file viewer. In the worksheet there is an explanation 
of the contents of the .txt files which is reproduced at the bottom of this file. The contents of the .txt files were calculated using the program 
Maple running on the Sun Ultra-80 computers of the High Performance Computing service of the ITS at the University of Durham. We should
mention that these calculations used the tables of knot diagrams contained in the program "Knotscape" by J. Hoste and M.B. Thistlethwaite
(entry [12] in thesis bibliography).

The other Maple worksheet, Algorithms.mws, contains implementations of the algorithms described in the thesis. These are the algorithms
that were used to calculate the .txt files.

Explanation of the .txt files:

The .txt files contain the Chatelet generators of the Alexander ideals of all the prime knots of up to 14 crossings. They were obtained by 
running the Seifert matrix and Chatelet basis algorithms described in the thesis on the tables of diagram encodings of diagrams of prime 
knots contained in Hoste & Thistlethwaite's program Knotscape, entry [12] in the thesis bibliography. There is one file for each of the 
crossing numbers 3..14 and then a file knots1-14.txt containing all of the knots of up to 14 crossings. 

The first line of each file is a Maple list [n], where n is the number of knots in that file. Then each subsequent line contains a maple list K, 
containing the Chatelet bases of the Alexander ideals of a knot. K is structures as follows. (n.b. The entries of a maple list are seperated 
by commas and enclosed in square brackets. The i-th entry of the list K is referred to by K[i].). 

K[1] is the crossing number of the knot, K[2] is 0 or 1 depending on whether the knot is alternating or non-alternating respectively, 
K[3] is the position of the knot in the Knotscape table, K[4] is the length of the chain of non-trivial Alexander ideals. Then K[4], K[5],.. etc 
is the chain of Alexander ideals, each one represented as a list of the Chatelet generators for the ideal. So K[4] always consists of a 
single element, the Alexander polynomial itself. The sequence K[4], K[5],.. etc terminates with the list [1] representing the first trivial ideal 
in the chain, all the ideals after that one being trivial as well of course. 

Example. The last line of the files 10cross.txt of the list

 [10, 1, 42, 2, [t^6-6*t^5+11*t^4-13*t^3+11*t^2-6*t+1], [7, t+1], [1]]

which represents the 42nd non-alternating 10 crossing prime knot. This knot has two non-trivial Alexander ideals the first of which is 
generated by the Alexander polynomial 

t^6-6*t^5+11*t^4-13*t^3+11*t^2-6*t+1

and the next ideal has Chatelet basis consisting of the polynomials 

 7, t+1

the third and subsequent ideals are the whole ring Z[t,t^-1].

