Module: sage.databases.jones
John Jones's tables of number fields
In order to use the Jones database, the optional database package must be installed using the SAGE command !sage -i database_jones_numfield
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.
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, 512), (4, -2048), (4, 256), (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 a with defining polynomial x^2 - 101, Number Field in a with defining polynomial x^4 - x^3 + 13*x^2 - 19*x + 361, Number Field in a with defining polynomial x^5 - x^4 - 40*x^3 - 93*x^2 - 21*x + 17, Number Field in a with defining polynomial x^5 + x^4 - 6*x^3 - x^2 + 18*x + 4, Number Field in a with defining polynomial x^5 + 2*x^4 + 7*x^3 + 4*x^2 + 11*x - 6]
Class: JonesDatabase
self) |
Functions: get,
ramified_at,
unramified_outside
self, S, [d=None], [var=a]) |
Return all fields in the database of degree d ramified exactly at the primes in S. Input:
sage: J = JonesDatabase() # requires optional package sage: J.ramified_at([101,119]) # requires optional package [] sage: J.ramified_at([119]) # requires optional package [] sage: J.ramified_at(101) # requires optional package [Number Field in a with defining polynomial x^2 - 101, Number Field in a with defining polynomial x^4 - x^3 + 13*x^2 - 19*x + 361, Number Field in a with defining polynomial x^5 - x^4 - 40*x^3 - 93*x^2 - 21*x + 17, Number Field in a with defining polynomial x^5 + x^4 - 6*x^3 - x^2 + 18*x + 4, Number Field in a with defining polynomial x^5 + 2*x^4 + 7*x^3 + 4*x^2 + 11*x - 6]
self, 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:
sage: J = JonesDatabase() # requires optional package sage: J.unramified_outside([101,119]) # requires optional package [Number Field in a with defining polynomial x - 1, Number Field in a with defining polynomial x^2 - 101, Number Field in a with defining polynomial x^4 - x^3 + 13*x^2 - 19*x + 361, Number Field in a with defining polynomial x^5 - x^4 - 40*x^3 - 93*x^2 - 21*x + 17, Number Field in a with defining polynomial x^5 + x^4 - 6*x^3 - x^2 + 18*x + 4, Number Field in a with defining polynomial x^5 + 2*x^4 + 7*x^3 + 4*x^2 + 11*x - 6]
Special Functions: __getitem__,
__init__,
__repr__,
_init,
_load
self, path) |
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:
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() sage: J._init() # not tested ... This takes about 5 seconds.
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