This document describes the tables included in this folder.



Each line of any given file represents a distinct number field and has the form

	D:G:r(x):g(x):parameters

where 

	- D is the discriminant of the field, 
	- G is the Galois group of the field,
	- r(x) is a polynomial for which the field is the splitting field (given by the PARI/GP function 'polredabs(f)'),
	- g(x) is the interesting factor of a biclique with the same splitting field as r(x),
	- 'parameters' is a list of parameters of a biclique with g(x) as its interesting factor.

The polynomials r(x) and g(x) are given by a lists of comma separated values, each value determining a coefficient of x.
They are listed in order from highest to lowest degree. 

The parameters field is formatted as follows.
For tables of quartic number fields, each field is the splitting field of the interesting factor of a (4,k)-biclique. 
The parameters are given in the order

	a1,a2,a3,a4,a12,a13,a14,a23,a24,a34,a123,a124,a134,a234,a1234

where the 4-clique is {v_1,v_2,v_3,v_4} and, for example, N(v_1,v_2,v_4) = a124.
For tables of quintic number fields, each field is the splitting field of the interesting factor of a (5,k)-biclique.
The parameters are given in the order.

	a1,a2,a3,a4,a5,a12,a13,a14,a15,a23,a24,a25,a34,a35,a45,a123,a124,a125,a134,a135,a145,a234,a235,a245,a345,a1234,a1235,a1245,a1345,a2345,a12345

where {v_1,v_2,v_3,v_4,v_5} is the 5-clique.



For example the line

	117:D(4):1,-1,-1,1,1:1,-19,140,-476,631:2,4,5,2,5,5,4,5,5,6,5,6,6,6,6

means that the (4,k)-biclique with 4-clique {v_1,v_2,v_3,v_4} and

	N(v_1)=2, N(v_2)=4, N(v_3)=5, N(v_4)=2, 
	N(v_1,v_2)=5, N(v_1,v_3)=5, N(v_1,v_4)=4, N(v_2,v_3)=5, N(v_2,v_4)=5, N(v_3,v_4)=6, 
	N(v_1,v_2,v_3)=5, N(v_1,v_2,v_4)=6, N(v_1,v_3,v_4)=6, N(v_2,v_3,v_4)=6, 
	N(v_1,v_2,v_3,v_4)=6

has interesting factor g(x)=x^4-19x^3+140x^2-476x+631, which has the same splitting fields as r(x)=x^4-x^3-x^2+x+1.
The splitting field of the interesting factor has discriminant 117 and Galois group D(4).



Filenames take the form 'Tn.r_1.r_2.d.txt' where
	
	- n is the degree of the polynomial for which each field is the splitting field,
	- (r_1,r_2) is the signature of the field,
	- d is the maximum absolute value of the discriminant of each number field.

The fields are sorted by their discriminants in ascending order.

For example, the file 'T4.0.2.10^5.txt' lists every quartic field with signature (0,2) and discriminant having absolute value less than or equal to 10^5.
For each field, a biclique that has that field as the splitting field of its interesting factor is given.

In the files 'T4.0.2.10^5.txt', 'T4.2.1.10^5.txt', and 'T4.4.0.10^5.txt', the smallest example of a biclique (in terms of both order and size)
that has each field as the splitting field of its interesting factor is given.
