This directory contains a stripped down version of the number field tables
published by the Bordeaux computational number theory group (H. Cohen,
F. Diaz y Diaz, M. Olivier and their students) around 1995, and incorporates
a number of corrections. The original [uncorrected] tables can be found at
ftp://megrez.math.u-bordeaux.fr/pub/numberfields/
AUTHORS: See ftp://megrez.math.u-bordeaux.fr/pub/numberfields/readme.pdf
for the authors of the original tables (~1995). The present version was
set up by Karim Belabas (Bordeaux) for the PARI group (2007).
FORMAT: The file T.gp contains data pertaining to fields of degree
3 <= n <= 7 with 0 <= r <= n real places. The data is in GP format, one
field per line, meant to be fed to the gp calculator as in
v = readvec("T31.gp");
which stores in the vector v (182417 elements) data corresponding to the
182417 complex cubic fields with discriminant > -10^6. Reading the largest
table requires a PARI stack size around 30M.
Entries in the resulting vector are sorted by increasing discriminant absolute
value. Each entry is a 4-components vector: [disc, V, h, cyc], where
* disc is the field discriminant.
* V is the VECTOR of coefficients of the minimal polynomial of a generator
of the number field. P = Pol(V) is the true defining polynomial, and
bnfinit(P) will recompute the bnf data associated to the field.
polgalois(P) indicates the Galois group of its Galois closure.
* h is the class number.
* cyc is the vector of orders of the class group cyclic components in
"elementary divisors" form: cyc = [d1, d2, ..., dk] means that
Cl(K) ~ (Z/d1 Z) x ... x (Z/dk Z), with dk | ... | d2 | d1.
NOTE 1: You need not download the whole table archive, all individual tables
are downloadable under
http://pari.math.u-bordeaux1.fr/pub/pari/packages/nftables/
NOTE 2: The tables were designed to include the minimal amount of data
necessary to recover all the invariants (V) as well as common filtering
criteria (disc, h, cyc). The most important information -- the hardest
to recover -- is the field equation.
NOTE 3: The time necessary to run bnfinit and polgalois on all the fields in
these tables is two to three hours. For this reason, the corresponding
output is no longer included in the tables, making them much smaller than
the historical version.
INDEX:
T20: |disc| < 10^6, 303968 fields
T22: |disc| < 10^6, 303957 fields
T31: |disc| < 10^6, 182417 fields
T33: |disc| < 2*10^6, 112444 fields
T40: |disc| < 10^6, 81322 fields
T42: |disc| < 10^6, 90671 fields
T44: |disc| < 10^6, 13073 fields
T51: |disc| <= 10^6, 28993 fields
T53: |disc| < 10^6, 10800 fields
T55: |disc| < 2*10^7, 22740 fields
T60: |disc| < 2*10^5, 442 fields
T62: |disc| < 4*10^5, 1179 fields
T64: |disc| < 10^6, 405 fields
T66: |disc| < 10^7, 398 fields
T71: |disc| < 6*10^5, 121 fields
T73: |disc| <18*10^5, 162 fields
T75: |disc| <12*10^6, 201 fields
T77: |disc| <15*10^7, 154 fields
ERRATUM: Here is the complete list of errors that are fixed in the
current version, compared to the original tables.
T20: disc = -75747, pol = x^2 - x + 18937: cyc = [24,2] [ was [12,4] ]
disc =-124323, pol = x^2 - x + 31081: cyc = [38,2] [ was [76] ]
disc =-186043, pol = x^2 - x + 46511: cyc = [24,2] [ was [12, 4] ]
T22: disc = 224108, pol = x^2 - 56027: h = 2 [ was 1 ]
disc = 404477, pol = x^2 - x - 101119: h = 2 [ was 1 ]
disc = 416597, pol = x^2 - x - 104149: cyc = [4] [ was [2] ]
disc = 485237, pol = x^2 - x - 121309: h = 2 [ was 1 ]
disc = 487805, pol = x^2 - x - 121951: h = 2 [ was 1 ]
T31: disc = -5979, pol = x^3 - 6*x - 45: h = 1 [ was 2 ]
disc = -53284, pol = x^3 - 59*x - 180: h = 1 [ was 2 ]
disc = -73251, pol = x^3 + 36*x - 355: h = 3 [ was 6 ]
T33: disc = 34620, pol = x^3 - x^2 - 56*x + 96: h = 1 [ was 2 ]