A database of Galois polynomials (v 4.0) ================================ This packages contains a database of polynomials defining Galois extensions of the rationals representing all abstract groups of order up to 143 for all signatures (3657 groups, 7194 polynomials). Abstract groups are indexed according to the GAP 4 small groups database <http://www.gap-system.org/Packages/sgl.html>. GAP4(a,b) denotes the group returned by SmallGroup(a,b) under GAP 4. a/nb: the number of abstract groups of order a a/b/name: a name for the group generated with GAP4 function StructureDescription. a/b/group: the underlying abstract group GAP4(a,b) in a format understandable by galoischartable. a/b/real: Vector [pol,den] where pol is a totally real Galois polynomial of Galois Group isomorphic to GAP4(a,b), and den is the common denominator of the conjugates returned by nfgaloisconj. a/b/complex: (a even) Vector [pol,den] where pol is a totally complex Galois polynomial of Galois Group isomorphic to GAP4(a,b), and den is the common denominator of the conjugates returned by nfgaloisconj. a/b/non-wss: if present, then the group GAP4(a,b) is not weakly super-solvable, see ??galoisinit. Bill Allombert and Igor Schein 2002-2018 ================================ Copyright © 2002-2018 The PARI Group We do not assert rights to the mathematical entities in this database. The group data are taken from GAP 4 and the SMALL GROUPS LIBRARY by Hans Ulrich Besche, Bettina Eick and Eamonn O'Brien. The database itself is licensed under the GNU GPL version 2 or latter.
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