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: # optional - database_kohel
sage: db = HilbertClassPolynomialDatabase()
sage: db[32]
x^2 - 52250000*x + 12167000000
>>> 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[source]#
Bases:
ClassPolynomialDatabase
The database of Atkin class polynomials.
- model = 'Atk'#
- class sage.databases.db_class_polynomials.DedekindEtaClassPolynomialDatabase[source]#
Bases:
ClassPolynomialDatabase
The database of Dedekind eta class polynomials.
- model = 'Eta'#
- class sage.databases.db_class_polynomials.HilbertClassPolynomialDatabase[source]#
Bases:
ClassPolynomialDatabase
The database of Hilbert class polynomials.
EXAMPLES:
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
>>> 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[source]#
Bases:
ClassPolynomialDatabase
The database of Weber class polynomials.