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 ]