def euler_p_factor(root_list, PREC):
''' computes the coefficients of the pth Euler factor expanded as a geometric series
ax^n is the Dirichlet series coefficient p^(-ns)
'''
PREC = floor(PREC)
# return satake_list
R = LaurentSeriesRing(CF, 'x')
x = R.gens()[0]
ep = prod([1 / (1 - a * x) for a in root_list])
return ep + O(x ** (PREC + 1))
def euler_p_factor(root_list, PREC):
''' computes the coefficients of the pth Euler factor expanded as a geometric series
ax^n is the Dirichlet series coefficient p^(-ns)
'''
PREC = floor(PREC)
# return satake_list
R = LaurentSeriesRing(CF, 'x')
x = R.gens()[0]
ep = prod([1 / (1 - a * x) for a in root_list])
return ep + O(x ** (PREC + 1))
