FieldsDB is a software package providing an interface to a database of number fields maintained by Tommy Hofmann and Carlo Sircana. It is written in julia and is based on the computer algebra system OSCAR. The development is supported by the Deutsche Forschungsgemeinschaft DFG within the Collaborative Research Center TRR 195.
Here is a quick example of using FieldsDB:
julia> using FieldsDB
...
julia> db = fields_database();
julia> lf = load_fields(db, degree = 2, discriminant_range = (fmpz(8), fmpz(8)))
1-element Vector{FieldsDB.DBField}:
Record of a number field
julia> K = number_field(lf[1])
Number field over Rational Field with defining polynomial x^2 - 2
julia> class_group(lf[1])
GrpAb: Z/1
julia> regulator(lf[1])
[0.8813735870195430252 +/- 6.76e-20]
julia> Qx, x = FlintQQ["x"];
julia> K, a = number_field(x^2+5, cached = false)
(Number field over Rational Field with defining polynomial x^2 + 5, _a)
julia> r = find_DBfield(db, K)
Record of a number field defined by x^2 + 5
julia> class_group(r)
GrpAb: Z/2
julia> h = hilbert_class_field(r)
Record of a number field
julia> number_field(h)
Number field over Rational Field with defining polynomial x^4 - 2*x^3 + x^2 + 5
julia> factor(discriminant(h))
1 * 5^2 * 2^4