Database of Hilbert polynomials

This module gives access to the database of Hilbert class polynomials. To use the database, you need to install the optional database_kohel package by the Sage command

sage -i database_kohel

EXAMPLES:

Sage

sage: # optional - database_kohel
sage: db = HilbertClassPolynomialDatabase()
sage: db[32]
x^2 - 52250000*x + 12167000000

Python

>>> from sage.all import *
>>> # optional - database_kohel
>>> db = HilbertClassPolynomialDatabase()
>>> db[Integer(32)]
x^2 - 52250000*x + 12167000000

AUTHORS:

• David Kohel (2006-08-04): initial version

class sage.databases.db_class_polynomials.AtkinClassPolynomialDatabase

Bases: ClassPolynomialDatabase

The database of Atkin class polynomials.

model = 'Atk'

class sage.databases.db_class_polynomials.ClassPolynomialDatabase

Bases: object

class sage.databases.db_class_polynomials.DedekindEtaClassPolynomialDatabase

Bases: ClassPolynomialDatabase

The database of Dedekind eta class polynomials.

model = 'Eta'

class sage.databases.db_class_polynomials.HilbertClassPolynomialDatabase

Bases: ClassPolynomialDatabase

The database of Hilbert class polynomials.

EXAMPLES:

Sage

sage: # optional - database_kohel
sage: db = HilbertClassPolynomialDatabase()
sage: db[-4]
x - 1728
sage: db[-7]
x + 3375
sage: f = db[-23]; f
x^3 + 3491750*x^2 - 5151296875*x + 12771880859375
sage: f.discriminant().factor()
-1 * 5^18 * 7^12 * 11^4 * 17^2 * 19^2 * 23
sage: db[-23]
x^3 + 3491750*x^2 - 5151296875*x + 12771880859375

Python

>>> from sage.all import *
>>> # optional - database_kohel
>>> db = HilbertClassPolynomialDatabase()
>>> db[-Integer(4)]
x - 1728
>>> db[-Integer(7)]
x + 3375
>>> f = db[-Integer(23)]; f
x^3 + 3491750*x^2 - 5151296875*x + 12771880859375
>>> f.discriminant().factor()
-1 * 5^18 * 7^12 * 11^4 * 17^2 * 19^2 * 23
>>> db[-Integer(23)]
x^3 + 3491750*x^2 - 5151296875*x + 12771880859375

model = 'Cls'

class sage.databases.db_class_polynomials.WeberClassPolynomialDatabase

Bases: ClassPolynomialDatabase

The database of Weber class polynomials.