8.2.1.2 JonesDatabase Objects

class JonesDatabase
JonesDatabase( [read_only=True])

Instances of class JonesDatabase have the following methods (in addition to inherited methods and special methods):

ramified_at,$  $ unramified_outside

These methods are defined as follows:

ramified_at( S, [d=None])

Return all fields in the database of degree d ramified exactly at the primes in S.

INPUT:
    S -- list or set of primes
    d -- None (default) or an integer

sage: J = JonesDatabase()
sage: J.ramified_at([101,119])
[]
sage: J.ramified_at([119])
[]
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]

unramified_outside( S, [d=None])

Return iterator over fields in the database of degree d unramified outside S. If d is omitted, return fields of any degree up to 6.

INPUT:
    S -- list or set of primes
    d -- None (default) or an integer

sage: J = JonesDatabase()
sage: J.unramified_outside([101,119])
[Number Field with defining polynomial x - 1, 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]

Instances of class JonesDatabase also have the following special methods:

__getitem__( S)

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