def calc_mu(k, x1, x2, x3, zeta, abel):
mu = []
for i in range(0, 4, 1):
mu.append(complex(
0.25 *pi* ((jtheta(1, abel[i]*pi, qfrom(k=k), 1) / (jtheta(1, abel[i]*pi, qfrom(k=k), 0)) )
+ (jtheta(3, abel[i]*pi, qfrom(k=k), 1) / (jtheta(3, abel[i]*pi, qfrom(k=k), 0)) )) \
- x3 - (x2 + complex(0,1) *x1) * zeta[i]))
return mu
def z_eta(u, m):
"""Jacobi eta function (eq 16.31.3, [Abramowitz]_)."""
q = qfrom(m=m)
DM = ellipk(m)
z = mp.pi * u / (2 * DM)
eta = jtheta(n=1, z=z, q=q)
return eta
def z_eta(u, m):
"""Jacobi eta function (eq 16.31.3, [Abramowitz]_)."""
q = qfrom(m=m)
DM = ellipk(m)
z = mp.pi * u / (2 * DM)
eta = jtheta(n=1, z=z, q=q)
return eta
def z_eta(u, m):
r"""
A function evaluate Jacobi eta function (eq 16.31.3, [Abramowitz]_).
:param u: Argument u
:param m: m is the elliptic parameter (not the modulus k and not the nome q)
:rtype: Returns a float, Jacobi eta function evaluated for the argument `u` and parameter `m`
"""
q = qfrom(m=m)
DM = ellipk(m)
z = mp.pi * u / (2 * DM)
eta = jtheta(n=1, z=z, q=q)
return eta
def z_eta(u, m):
r"""
A function evaluate Jacobi eta function (eq 16.31.3, [Abramowitz]_).
:param u: Argument u
:param m: m is the elliptic parameter (not the modulus k and not the nome q)
:rtype: Returns a float, Jacobi eta function evaluated for the argument `u` and parameter `m`
"""
q = qfrom(m=m)
DM = ellipk(m)
z = mp.pi * u / (2 * DM)
eta = jtheta(n=1, z=z, q=q)
return eta
def calc_eta_by_theta(k, z):
return 0.25 * complex(0, 1) * pi * ((jtheta(2, 0, qfrom(k=k), 0)) ** 2) \
* ((jtheta(4, 0, qfrom(k=k), 0)) ** 2) \
* (jtheta(3, 0, qfrom(k=k), 0)) \
* (jtheta(3, 2*z*pi, qfrom(k=k), 0)) \
/ ( ((jtheta(1, z*pi, qfrom(k=k), 0)) ** 2) * ((jtheta(3, z*pi, qfrom(k=k), 0)) ** 2) )
def calc_eta_by_theta(k, z):
return 0.25 * complex(0, 1) * pi * ((jtheta(2, 0, qfrom(k=k), 0)) ** 2) \
* ((jtheta(4, 0, qfrom(k=k), 0)) ** 2) \
* (jtheta(3, 0, qfrom(k=k), 0)) \
* (jtheta(3, 2*z*pi, qfrom(k=k), 0)) \
/ ( ((jtheta(1, z*pi, qfrom(k=k), 0)) ** 2) * ((jtheta(3, z*pi, qfrom(k=k), 0)) ** 2) )