def __init__(self, E, m):
if E.has_cm():
raise ValueError("E should not be cm")
from sympowlmfdb import sympowlmfdb
bad_primes, conductor, root_number = sympowlmfdb.local_data(E, m)
self.bad_prime_euler = {}
self.bad_primes = [i for (i, _) in bad_primes]
for j in bad_primes:
a, b = j
self.bad_prime_euler[a] = b
self.m = m
self.conductor = conductor
self.root_number = root_number
self.E = E
self._construct_L()
def __init__(self, E, m):
if E.has_cm():
raise ValueError("E should not be cm")
from sympowlmfdb import sympowlmfdb
bad_primes, conductor, root_number = sympowlmfdb.local_data(E, m)
self.bad_prime_euler = {}
self.bad_primes = [i for (i, _) in bad_primes]
for j in bad_primes:
a, b = j
self.bad_prime_euler[a] = b
self.m = m
self.conductor = conductor
self.root_number = root_number
self.E = E
self._construct_L()
def symmetricEulerFactor(E, m, p):
bad_primes, conductor, root_number = sympowlmfdb.local_data(E, m)
bad_P_poly = {}
bad_P_list = [i for (i, _) in bad_primes]
for j in bad_primes:
a, b = j
bad_P_poly[a] = b
if p in bad_P_list:
return bad_P_poly[p]
m = sage.rings.all.Integer(m)
# E=EllipticCurve(E)
R = sage.rings.all.PolynomialRing(sage.rings.all.RationalField(), 't')
t = R('t')
F = 1
print type(F)
for i in range(0, (m - 1) / 2 + 1):
s = m - 2 * i
s2 = s // 2
ap = E.ap(p)
TI = sum([
tbin(s, s2 - k) * ap**(2 * k) * p**(s2 - k)
for k in xrange(0, s2 + 1)
])
if s % 2 != 0:
TI = ap * TI
F = F * (1 - TI * p**i * t + p**m * t**2)
if m % 2 == 0:
F = F * (1 - p**(m / 2) * t)
return F.coeffs()
def symmetricEulerFactor(E, m, p):
bad_primes, conductor, root_number = sympowlmfdb.local_data(E, m)
bad_P_poly = {}
bad_P_list = [i for (i, _) in bad_primes]
for j in bad_primes:
a, b = j
bad_P_poly[a] = b
if p in bad_P_list:
return bad_P_poly[p]
m = sage.rings.all.Integer(m)
# E=EllipticCurve(E)
R = sage.rings.all.PolynomialRing(sage.rings.all.RationalField(), 't')
t = R('t')
F = 1
print type(F)
for i in range(0, (m - 1) / 2 + 1):
s = m - 2 * i
s2 = s // 2
ap = E.ap(p)
TI = sum([tbin(s, s2 - k) * ap ** (2 * k) * p ** (s2 - k) for k in xrange(0, s2 + 1)])
if s % 2 != 0:
TI = ap * TI
F = F * (1 - TI * p ** i * t + p ** m * t ** 2)
if m % 2 == 0:
F = F * (1 - p ** (m / 2) * t)
return F.coeffs()
def symmetricPowerLfunction(E, n):
"""
gives lcalc version of symmetric power L function
"""
bad_primes, conductor, root_number = sympowlmfdb.local_data(E, n)
def symmetricPowerLfunction(E, n):
"""gives lcalc version of symmetric power L function"""
bad_primes, conductor, root_number = sympowlmfdb.local_data(E, n)