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| README | H A D | 25-Jun-2018 | 1.5 KiB | 44 | 28 |
README
1A database of Galois polynomials (v 4.0)
2================================
3
4This packages contains a database of polynomials defining Galois extensions of
5the rationals representing all abstract groups of order up to 143 for
6all signatures (3657 groups, 7194 polynomials).
7
8Abstract groups are indexed according to the GAP 4 small groups database
9<http://www.gap-system.org/Packages/sgl.html>.
10GAP4(a,b) denotes the group returned by SmallGroup(a,b) under GAP 4.
11
12a/nb: the number of abstract groups of order a
13
14a/b/name: a name for the group generated with GAP4 function
15StructureDescription.
16
17a/b/group: the underlying abstract group GAP4(a,b) in a format understandable
18by galoischartable.
19
20a/b/real: Vector [pol,den] where pol is a totally real Galois polynomial
21of Galois Group isomorphic to GAP4(a,b), and den is the common denominator
22of the conjugates returned by nfgaloisconj.
23
24a/b/complex: (a even) Vector [pol,den] where pol is a totally complex
25Galois polynomial of Galois Group isomorphic to GAP4(a,b), and den is the
26common denominator of the conjugates returned by nfgaloisconj.
27
28a/b/non-wss: if present, then the group GAP4(a,b) is not weakly super-solvable,
29see ??galoisinit.
30
31Bill Allombert and Igor Schein 2002-2018
32
33================================
34
35Copyright © 2002-2018 The PARI Group
36
37We do not assert rights to the mathematical entities in this database.
38
39The group data are taken from GAP 4 and the SMALL GROUPS LIBRARY by Hans Ulrich
40Besche, Bettina Eick and Eamonn O'Brien.
41
42The database itself is licensed under the GNU GPL version 2 or latter.
43
44