This is a table of number fields with bounded ramification and degree
.
You can query the database for all number fields in Jones's tables
with bounded ramification and degree.
See Also:
These tables were downloaded fromFirst 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, 1)]
List all fields in the database ramified at 101
sage: J.ramified_at(101) [Number Field with defining polynomial x^2 - 101, Number Field with defining polynomial x^4 - x^3 + 13*x^2 - 19*x + 361, Number Field with defining polynomial x^5 + 2*x^4 + 7*x^3 + 4*x^2 + 11*x - 6, Number Field with defining polynomial x^5 + x^4 - 6*x^3 - x^2 + 18*x + 4, Number Field with defining polynomial x^5 - x^4 - 40*x^3 - 93*x^2 - 21*x + 17]
The module tables.jones defines the following classes: