13.2.1.2 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

Further documentation:

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 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]

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 in x with defining polynomial x - 1, 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]

Instances of class JonesDatabase also have the following special methods:

__getitem__,$  $ __repr__,$  $ _init,$  $ _load

Further documentation:

_init( [path=/home/was/sage/data/src/jones_data/])

Create the database from scratch from the PARI files on John Jone's web page, downloaded (e.g., via wget) to a local directory, which is specified as path above.

INPUT:
    -- (default works on William Stein install.)
        path must be the path to Jone's Number_Fields directory
          http://hobbes.la.asu.edu/Number_Fields
       These files should have been downloaded using wget.

This is how to create the database from scratch, assuming that the number fields are in the default directory above: From a cold start of SAGE:

    sage: J = JonesDatabase(read_only=False)
    sage: J._init()
    ...
This takes about 5 seconds.

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