def signOfEmfLfunction(level, weight, coefs, tol=10**(-7), num=1.3):
""" Computes the sign of a EMF with give level, weight and
coefficients numerically by computing the value of the EMF
at two points related by the Atkin-Lehner involution.
If the absolute value of the result is more than tol from 1
then it returns "Not able to compute" which indicates to few
(or wrong) coeffcients.
The parameter num chooses the related points and shouldn't be 1.
"""
sum1 = 0
sum2 = 0
for i in range(1, len(coefs)):
sum1 += coefs[i - 1] * math.exp(
-2 * math.pi * i * num / math.sqrt(level))
logger.debug("Sum1: {0}".format(sum1))
sum2 += coefs[i - 1].conjugate() * math.exp(- 2 * math.pi * i / num / math.sqrt(level)) / \
num ** weight
logger.debug("Sum2: {0}".format(sum2))
sign = sum1 / sum2
if abs(abs(sign) - 1) > tol:
logger.critical(
"Not enough coefficients to compute the sign of the L-function.")
sign = "Not able to compute."
sign = 1 # wrong, but we need some type of error handling here.
return sign
def signOfEmfLfunction(level, weight, coefs, tol=10 ** (-7), num=1.3):
""" Computes the sign of a EMF with give level, weight and
coefficients numerically by computing the value of the EMF
at two points related by the Atkin-Lehner involution.
If the absolute value of the result is more than tol from 1
then it returns "Not able to compute" which indicates to few
(or wrong) coeffcients.
The parameter num chooses the related points and shouldn't be 1.
"""
sum1 = 0
sum2 = 0
for i in range(1, len(coefs)):
sum1 += coefs[i - 1] * math.exp(-2 * math.pi * i * num / math.sqrt(level))
logger.debug("Sum1: {0}".format(sum1))
sum2 += coefs[i - 1].conjugate() * math.exp(-2 * math.pi * i / num / math.sqrt(level)) / num ** weight
logger.debug("Sum2: {0}".format(sum2))
sign = sum1 / sum2
if abs(abs(sign) - 1) > tol:
logger.critical("Not enough coefficients to compute the sign of the L-function.")
sign = "Not able to compute."
return sign
