Coverage for local/lib/python2.7/site-packages/sage/databases/db_modular_polynomials.py : 29%
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""" Database of Modular Polynomials """ ####################################################################### # Copyright (C) 2006 William Stein <wstein@gmail.com> # Copyright (C) 2006 David Kohel <kohel@maths.usyd.edu.au> # Copyright (C) 2016 Vincent Delecroix <vincent.delecroix@labri.fr> # # Distributed under the terms of the GNU General Public License (GPL) # as published by the Free Software Foundation; either version 2 of # the License, or (at your option) any later version. # http://www.gnu.org/licenses/ #*****************************************************************************
from __future__ import print_function, absolute_import
def _dbz_to_string(name): r""" TESTS::
sage: from sage.databases.db_modular_polynomials import _dbz_to_string sage: _dbz_to_string('PolMod/Atk/pol.002.dbz') # optional - database_kohel '3 0 1 \n2 1 -1 \n2 0 744 \n1 1 -1 \n1 0 184512 \n0 2 1 \n0 1 7256 \n0 0 15252992 \n' sage: _dbz_to_string('PolMod/Cls/pol.001.dbz') # optional - database_kohel '1 0 1 \n' sage: _dbz_to_string('PolMod/Eta/pol.002.dbz') # optional - database_kohel '3 0 1 \n2 0 48 \n1 1 -1 \n1 0 768 \n0 0 4096 \n' sage: _dbz_to_string('PolMod/EtaCrr/crr.02.002.dbz') # optional - database_kohel '2 1 1 \n2 0 -48 \n1 1 2304 \n0 2 -4096 \n0 1 196608 \n' sage: _dbz_to_string('PolHeeg/Cls/0000001-0005000/pol.0000003.dbz') # optional - database_kohel '0\n1\n' """
data = bz2.decompress(f.read())
return data
def _dbz_to_integer_list(name): r""" TESTS::
sage: from sage.databases.db_modular_polynomials import _dbz_to_integer_list sage: _dbz_to_integer_list('PolMod/Atk/pol.002.dbz') # optional - database_kohel [[3, 0, 1], [2, 1, -1], [2, 0, 744], [1, 1, -1], [1, 0, 184512], [0, 2, 1], [0, 1, 7256], [0, 0, 15252992]] sage: _dbz_to_integer_list('PolMod/Cls/pol.001.dbz') # optional - database_kohel [[1, 0, 1]] sage: _dbz_to_integer_list('PolMod/Eta/pol.002.dbz') # optional - database_kohel [[3, 0, 1], [2, 0, 48], [1, 1, -1], [1, 0, 768], [0, 0, 4096]] """ from sage.rings.integer import Integer data = _dbz_to_string(name) return [[Integer(v) for v in row.strip().split(" ")] for row in data.split("\n")[:-1]]
def _dbz_to_integers(name): r""" TESTS::
sage: from sage.databases.db_modular_polynomials import _dbz_to_integers sage: _dbz_to_integers('PolHeeg/Cls/0000001-0005000/pol.0000003.dbz') # optional - database_kohel [0, 1] """
class ModularPolynomialDatabase: def _dbpath(self, level): r""" TESTS::
sage: C = ClassicalModularPolynomialDatabase() sage: C._dbpath(3) 'PolMod/Cls/pol.003.dbz' sage: C._dbpath(8) 'PolMod/Cls/pol.008.dbz' """
def __repr__(self): r""" EXAMPLES::
sage: ClassicalModularPolynomialDatabase() Classical modular polynomial database
sage: DedekindEtaModularPolynomialDatabase() Dedekind eta modular polynomial database sage: DedekindEtaModularPolynomialDatabase() Dedekind eta modular polynomial database
sage: AtkinModularPolynomialDatabase() Atkin modular polynomial database """
poly = "correspondence" else:
def __getitem__(self, level): """ Return the modular polynomial of given level, or an error if there is no such polynomial in the database.
EXAMPLES::
sage: DBMP = ClassicalModularPolynomialDatabase() sage: f = DBMP[29] # optional - database_kohel sage: f.degree() # optional - database_kohel 58 sage: f.coefficient([28,28]) # optional - database_kohel 400152899204646997840260839128
sage: DBMP[50] # optional - database_kohel Traceback (most recent call last): ... LookupError: filename .../kohel/PolMod/Cls/pol.050.dbz does not exist """ from sage.rings.integer import Integer from sage.rings.integer_ring import IntegerRing from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
if self.model in ("Atk","Eta"): level = Integer(level) if not level.is_prime(): raise TypeError("Argument level (= %s) must be prime."%level) elif self.model in ("AtkCrr","EtaCrr"): N = Integer(level[0]) if not N in (2,3,5,7,13): raise TypeError("Argument level (= %s) must be prime."%N) modpol = self._dbpath(level) coeff_list = _dbz_to_integer_list(modpol) if self.model == "Cls": P = PolynomialRing(IntegerRing(),2,"j") else: P = PolynomialRing(IntegerRing(),2,"x,j") poly = {} if self.model == "Cls": if level == 1: return P({(1,0):1,(0,1):-1}) for cff in coeff_list: i = cff[0] j = cff[1] poly[(i,j)] = Integer(cff[2]) if i != j: poly[(j,i)] = Integer(cff[2]) else: for cff in coeff_list: poly[(cff[0],cff[1])] = Integer(cff[2]) return P(poly)
class ModularCorrespondenceDatabase(ModularPolynomialDatabase): def _dbpath(self,level): r""" TESTS::
sage: DB = DedekindEtaModularCorrespondenceDatabase() sage: DB._dbpath((2,4)) 'PolMod/EtaCrr/crr.02.004.dbz' """
class ClassicalModularPolynomialDatabase(ModularPolynomialDatabase): """ The database of classical modular polynomials, i.e. the polynomials Phi_N(X,Y) relating the j-functions j(q) and j(q^N). """ model = "Cls"
class DedekindEtaModularPolynomialDatabase(ModularPolynomialDatabase): """ The database of modular polynomials Phi_N(X,Y) relating a quotient of Dedekind eta functions, well-defined on X_0(N), relating x(q) and the j-function j(q). """ model = "Eta"
class DedekindEtaModularCorrespondenceDatabase(ModularCorrespondenceDatabase): """ The database of modular correspondences in $X_0(p) \times X_0(p)$, where the model of the curves $X_0(p) = \Bold{P}^1$ are specified by quotients of Dedekind's eta function. """ model = "EtaCrr"
class AtkinModularPolynomialDatabase(ModularPolynomialDatabase): """ The database of modular polynomials Phi(x,j) for $X_0(p)$, where x is a function on invariant under the Atkin-Lehner invariant, with pole of minimal order at infinity. """ model = "Atk"
class AtkinModularCorrespondenceDatabase(ModularCorrespondenceDatabase): model = "AtkCrr" |