Source of global number field data (reviewed)

Number fields were drawn from the following sources.

The PARI database from the Bordeaux PARI group [pari.math.u-bordeaux.fr/pub/numberfields/], which in turn, was a combination of work by several authors:

• M. Olivier for degree 3 fields;
• J. Buchmann, D. Ford, and M. Pohst for degree 4 fields [MR:1176706];
• A. Schwarz, M. Pohst, and F. Diaz y Diaz for degree 5 fields [MR:1219705];
• M. Olivier for degree 6 fields [MR:1106977], [MR:1149805], [MR:1116107], [MR:1096589], [MR:1061760], [MR:1050276], and with A.-M. Bergé and J. Martinet [MR:1011438];
• P. Létard for degree 7 fields.

Totally real fields of degrees from 6 to 10 computed by John Voight [arXiv:0802.0194, math.dartmouth.edu/~jvoight/nf-tables/index.html].

Almost totally real fields computed by John Voight. [arXiv:1408.2001, MR:3384884].

Fields from John Jones-David Roberts database. [arXiv:1404.0266, MR:3356048, hobbes.la.asu.edu/NFDB].

Fields from Jürgen Klüners-Gunter Malle database. [arXiv:math/0102232, galoisdb.math.upb.de/].

Complete lists of global number fields were computed using two techniques, Hunter searches (see Section 9.3 of [MR:1728313, 10.1007/978-1-4419-8489-0]) and class field theory (see Chapter 5 and Section 9.2 of [MR:1728313, 10.1007/978-1-4419-8489-0]). Hunter searches are named for named for John Hunter [MR:0091309], whose technique was refined significantly by M. Pohst [MR:0644904]. In some cases, the Hunter searches are "targeted" in that they focused on specific prime ramification [MR:1986816, 10.1090/S0025-5718-03-01510-2].