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<n><r>.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 commonly filtering
criteria (disc, h, cyc). The most important information -- the one which is
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 ]
