def attach_new_label(f):
print f['label']
F = hmf_fields.find_one({"label": f['field_label']})
P = PolynomialRing(Rationals(), 'w')
# P is used implicitly in the eval() calls below. When these are
# removed, this will not longer be neceesary, but until then the
# assert statement is for pyflakes.
assert P
if type(f['level_ideal']) == str or type(f['level_ideal']) == unicode:
N = eval(f['level_ideal'])
else:
N = f['level_ideal']
if type(N) != list or len(N) != 3:
print f, N, type(N)
raise ValueError("{} does not define a valid level ideal".format(N))
f['level_ideal'] = [N[0], N[1], str(N[2])]
try:
ideal_label = F['ideal_labels'][F['ideals'].index(f['level_ideal'])]
f['level_ideal_label'] = ideal_label
f['label'] = parse_label(f['field_label'], f['weight'],
f['level_ideal_label'], f['label_suffix'])
hmf_forms.save(f)
print f['label']
except ValueError:
hmf_forms.remove(f)
print "REMOVED!"
def attach_new_label(f):
print(f['label'])
F = hmf_fields.find_one({"label": f['field_label']})
P = PolynomialRing(Rationals(), 'w')
# P is used implicitly in the eval() calls below. When these are
# removed, this will not longer be necessary, but until then the
# assert statement is for pyflakes.
assert P
if isinstance(f['level_ideal'], str):
N = eval(f['level_ideal'])
else:
N = f['level_ideal']
if type(N) != list or len(N) != 3:
print(f, N, type(N))
assert False
f['level_ideal'] = [N[0], N[1], str(N[2])]
try:
ideal_label = F['ideal_labels'][F['ideals'].index(f['level_ideal'])]
f['level_ideal_label'] = ideal_label
f['label'] = construct_full_label(f['field_label'], f['weight'],
f['level_ideal_label'],
f['label_suffix'])
hmf_forms.save(f)
print(f['label'])
except ValueError:
hmf_forms.remove(f)
print("REMOVED!")
def endomorphism_frob(f):
r"""
INPUT:
- ``f`` -- a Frobenius polynomial of an Abelian variety
OUTPUT: A tuple:
- dim_Q ( End(A^{al} )
- k, the degree of field ext where all endomorphism are defined
- a sorted list that represents the geometric isogeny decomposition
over an algebraic closure.
Let
A^{al} = (A_1)^n_1 x ... x (A_k)^n_t
and write
det(1 - T Frob^k | H^1(Ai^n_i)) = c_i (T)^m_i.
Then we return:
[ (m_i, m_i * deg(c_i), c_i) for i in range(1, t) ].
"""
if f(0) != 1:
f = f.reverse()
assert f(0) == 1
g = f.degree() / 2
flist = f.list()
q = Integers()(flist[-1]).nth_root(g)
T = f.parent().gen()
fof = tensor_charpoly(f, f)
g = fof.change_ring(Rationals())(T / q)
dimtotal = 0
fieldext = 1
for factor, power in g.factor():
iscyclo = factor.is_cyclotomic(certificate=True)
if iscyclo > 0:
dimtotal += power * factor.degree()
fieldext = LCM(fieldext, iscyclo)
fext = power_charpoly(f, fieldext)
endo = sorted([(power, power * factor.degree(), factor)
for factor, power in fext.factor()])
return dimtotal, fieldext, endo
def repair_fields(D):
F = hmf_fields.find_one({"label": '2.2.' + str(D) + '.1'})
P = PolynomialRing(Rationals(), 'w')
# P is used implicitly in the eval() calls below. When these are
# removed, this will not longer be neceesary, but until then the
# assert statement is for pyflakes.
assert P
primes = F['primes']
primes = [[int(eval(p)[0]), int(eval(p)[1]), str(eval(p)[2])] for p in primes]
F['primes'] = primes
hmff = file("data_2_" + (4 - len(str(D))) * '0' + str(D))
# Parse field data
for i in range(7):
v = hmff.readline()
ideals = eval(v[10:][:-2])
ideals = [[p[0], p[1], str(p[2])] for p in ideals]
F['ideals'] = ideals
hmf_fields.save(F)
# -*- coding: utf-8 -*-
from __future__ import print_function
from sage.misc.preparser import preparse
from sage.interfaces.magma import magma
from sage.all import PolynomialRing, Rationals
from lmfdb.base import getDBConnection
C = getDBConnection()
hmf_forms = C.hmfs.forms
hmf_fields = C.hmfs.fields
fields = C.numberfields.fields
P = PolynomialRing(Rationals(), 3, ['w', 'e', 'x'])
w, e, x = P.gens()
def recompute_AL(field_label=None, skip_odd=False):
if field_label is None:
S = hmf_forms.find({"AL_eigenvalues_fixed": None})
else:
S = hmf_forms.find({"field_label": field_label, "AL_eigenvalues_fixed": None})
S = S.sort("label")
field_label = None
magma.eval('SetVerbose("ModFrmHil", 1);')
v = S.next()
while True:
NN_label = v["level_label"]
v_label = v["label"]
The authors can be reached at: [email protected] and [email protected]. ==================================================================== """ from sage.all import PolynomialRing, Rationals, prod, oo from sage.arith.misc import primes from sage.combinat.permutation import Permutation from sage.groups.additive_abelian.additive_abelian_group import AdditiveAbelianGroup from sage.groups.perm_gps.permgroup import PermutationGroup from sage.groups.perm_gps.permgroup_named import TransitiveGroup, SymmetricGroup R = PolynomialRing(Rationals(), "x") x = R.gen() EC_Q_ISOGENY_PRIMES = {2, 3, 5, 7, 11, 13, 17, 19, 37, 43, 67, 163} CLASS_NUMBER_ONE_DISCS = {-3, -4, -7, -8, -11, -19, -43, -67, -163} SMALL_GONALITIES = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 47, 59, 71} # Global methods def weil_polynomial_is_elliptic(f, q, a): """ On input of a polynomial f that is a weil polynomial of degree 2 and has constant term q^a we check if it actually comes from an elliptic curve over GF(q^a). This uses theorem 4.1 of http://archive.numdam.org/article/ASENS_1969_4_2_4_521_0.pdf """ if f[1] % q != 0:
QuadraticField,
log,
exp,
find_root,
ceil,
NumberField,
hilbert_class_polynomial,
RR,
EllipticCurve,
lcm,
gcd,
)
# Global constants
R = PolynomialRing(Rationals(), "x") # used in many functions
# The constant which Momose calls Q_2
Q_2 = 7
# Various other Quantities
GENERIC_UPPER_BOUND = 10 ** 30
EC_Q_ISOGENY_PRIMES = {2, 3, 5, 7, 11, 13, 17, 19, 37, 43, 67, 163}
CLASS_NUMBER_ONE_DISCS = {-1, -2, -3, -7, -11, -19, -43, -67, -163}
# The NotTypeOneTwo epsilons, up to Galois and dual action, with their types
EPSILONS_NOT_TYPE_1_2 = {
(0, 12): "quadratic",
(0, 4): "sextic",
(0, 8): "sextic",
(4, 4): "sextic-constant",
