def naive_padic_H_value(self, p, t, verbose=False):
R = GF(p)
t = R(t)
interval_sums = {}
denominator = self.pochhammer_numerator_alphas_betas(p, 0)
interval_sums[0] = 0 if self.D else 1
for i, v in enumerate(self.pshift):
start = self.starts[i]
end = self.ends[i]
# deals with the start point
m = start * (p - 1)
if start > 0 and m.is_integer():
m = ZZ(m)
# FIXME do the math to assert that is true
assert self.pshift[i - 1] - self.beta().count(
start
) >= 0, "i = %s start = %s self.pshift[i-i] = %s, self.beta().count(start) = %s" % (
i, start, self.pshift[i - 1], self.beta().count(start))
# eta at the end of the previous interval
eta_m = self.zigzag(start) + self.beta().count(
start) - self.alpha().count(start)
xi_m = self.beta().count(0) - self.beta().count(start)
#print("etaxi", start, end, m, eta_m, xi_m)
if eta_m + xi_m + self.D == 0:
sign = -1 if eta_m % 2 else 1
#print(start, sign)
interval_sums[
start] = sign * self.pochhammer_numerator_alphas_betas(
p, m, verbose) * t**m / denominator
# deal with middle of the interval and the end point
if v == 0:
sign = -1 if self.zigzag(start) % 2 else 1
#print((start, end), sign)
interval_sums[(
start, end)] = self.naive_padic_H_value_interval_numerator(
p, t, start, end, sign * denominator, verbose)
# deals with the end point
m = end * (p - 1)
# if m.is_integer() then it is handled as a start
if end != 1 and not m.is_integer():
m = floor(m)
interval_sums[
end] = sign * self.pochhammer_numerator_alphas_betas(
p, m, verbose) * t**m / denominator
if verbose:
print(interval_sums)
return sum(interval_sums.values())
