13.2.1 databases.jones - John Jones's tables of number fields

This is a table of number fields with bounded ramification and degree $ \leq 6$ . You can query the database for all number fields in Jones's tables with bounded ramification and degree.

See Also:

These tables were downloaded from
http://hobbes.la.asu.edu/Number_Fields

First load the database:

sage: J = JonesDatabase()
sage: J
John Jones's table of number fields with bounded ramification and degree <=
6

List the degree and discriminant of all fields in the database that have ramification at most at 2:

sage: [(k.degree(), k.disc()) for k in J.unramified_outside([2])]
[(1, 1), (2, 8), (2, -4), (2, -8), (4, -2048), (4, -1024), (4, 256), (4,
2048), (4, 512), (4, 2048), (4, 2048)]

List the discriminants of the fields of degree exactly 2 unramified outside 2:

sage: [k.disc() for k in J.unramified_outside([2],2)]
[8, -4, -8]

List the discriminants of cubic field in the database ramified exactly at 3 and 5:

sage: [k.disc() for k in J.ramified_at([3,5],3)]
[-6075, -6075, -675, -135]
sage: factor(6075)
3^5 * 5^2
sage: factor(675)
3^3 * 5^2
sage: factor(135)
3^3 * 5

List all fields in the database ramified at 101

sage: J.ramified_at(101)
[Number Field in x with defining polynomial x^2 - 101, Number Field in x
with defining polynomial x^4 - x^3 + 13*x^2 - 19*x + 361, Number Field in x
with defining polynomial x^5 + 2*x^4 + 7*x^3 + 4*x^2 + 11*x - 6, Number
Field in x with defining polynomial x^5 + x^4 - 6*x^3 - x^2 + 18*x + 4,
Number Field in x with defining polynomial x^5 - x^4 - 40*x^3 - 93*x^2 -
21*x + 17]

The module databases.jones defines the following classes:

class IntegerRing
The ring of integers.

class JonesDatabase

class RationalField
The class RationalField represents the field $ \mathbf{Q}$ of rational numbers.



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