def norm(self, order):
# TODO: Who is n?
n = None
if order < 0:
return 0
else:
return (
qp(self.q, self.q, order) *
qp(-self.p * self.q ** (self.N + 1), self.q, order) *
qp(-self.p, self.q, order) ** -1 *
qp(self.q ** -self.N, self.q, order) ** -1 *
(1 + self.p) / (1 + self.p * self.q ** (2 * order)) *
qp(-self.p * self.q, self.q, self.N) *
self.p ** -self.N * self.q ** -special.binom(self.N + 1, 2) *
(-self.p * self.q ** -self.N) ** order *
self.q ** order ** 2
)
return (
qp(self.q, self.q, n) *
qp(-self.p * self.q ** (self.N + 1), self.q, n) *
qp(-self.p, self.q, n) ** -1 *
qp(self.q ** -self.N, self.q, n) ** -1 *
(1 + self.p) / (1 + self.p * self.q ** (2 * n)) *
qp(-self.p * self.q, self.q, self.N) *
self.p ** -self.N * self.q ** -special.binom(self.N + 1, 2) *
(-self.p * self.q ** -self.N) ** n *
self.q ** n ** 2
)
def weight(self, x):
mp.dps = 25
mp.pretty = True
return (
qp(self.q ** -self.N, self.q, x) *
qp(self.q, self.q, x) ** -1 *
(-self.p) ** -x
)
def weight(self, x):
mp.dps = 25
mp.pretty = True
return (
qp(self.alpha * self.q, self.q, x) *
qp(self.q ** -self.N, self.q, x) *
(self.alpha * self.beta * self.q) ** -x *
qp(self.q, self.q, x) ** -1 *
qp(self.beta ** -1 * self.q ** -self.N, self.q, x) ** -1
)
def norm(self, order):
if order < 0:
return 0
else:
return (
qp(self.alpha * self.beta * self.q ** 2, self.q, self.N) *
qp(self.q, self.q, order) *
qp(
self.alpha *
self.beta *
self.q ** (self.N + 2),
self.q,
order
) *
qp(self.beta * self.q, self.q, order) *
qp(self.beta * self.q, self.q, self.N) ** -1 *
qp(self.alpha * self.q, self.q, order) ** -1 *
qp(self.alpha * self.beta * self.q, self.q, order) ** -1 *
qp(self.q ** -self.N, self.q, order) ** -1 *
(self.alpha * self.q) ** -self.N *
(1 - self.alpha * self.beta * self.q) *
(-self.alpha * self.q) ** order *
(1 - self.alpha * self.beta * self.q ** (2 * order + 1)) **
-1 * self.q ** (special.binom(order, 2) - self.N * order)
)
def weight(self, x):
mp.dps = 25
mp.pretty = True
return (
self.a ** x /
qp(self.q, self.q, x) *
self.q ** special.binom(x, 2)
)
def keval(self, x, k, order):
mp.dps = 25
mp.pretty = True
return (
self.q ** k *
qp(self.q ** -order, self.q, k) *
qp(self.alpha * self.beta * self.q ** (order + 1), self.q, k) *
qp(self.q ** -x, self.q, k) *
qp(self.alpha * self.q, self.q, k) ** -1 *
qp(self.q ** -self.N, self.q, k) ** -1 /
qp(self.q, self.q, k)
)
def keval(self, x, k, order):
mp.dps = 25
mp.pretty = True
return (
self.q ** k *
qp(self.q ** -order, self.q, k) *
qp(self.q ** -x, self.q, k) *
qp(-self.p * self.q ** order, self.q, k) *
qp(self.q ** -self.N, self.q, k) ** -1 *
qp(0, self.q, k) ** -1 *
qp(self.q, self.q, k) ** -1
)
def eta(tau):
return exp(j * pi * tau / 12) * qp(exp(2 * pi * j * tau),
exp(2 * pi * j * tau))