I'm having trouble with getting a complex approximation to a QQbar number.
We're working with symmetric polynomials of multipliers of periodic points,
so the numbers generated are complicated and the failure occurs fairly far
along in the computation, so the code to generate the error is a little
complicated. The issue is that I'm getting a 'maximum recursion depth
error' when trying to get any kind of numerical approximation to the
number. The code below will produce the error. I've tried looking through
the qqbar.py file and am having trouble isolating exactly what the issue
is. If someone knowledgeable about the QQbar/CIF code could give a suggest
on how to get a numerical approximation of these numbers that would be
appreciated (working from the start with complex number leads to too much
error after iteration, and working with the resulting QQbar numbers is too
slow)
Thanks,
Ben
A.<z> = AffineSpace(QQ,1)
H = End(A)
f = H([z^2 + 3/4])
n = 6
type = 6
d = f.nth_iterate_map(n)._polys[0].univariate_polynomial().derivative(z)
roots = (f.nth_iterate_map(n)._polys[0].univariate_polynomial() -
z).univariate_polynomial().roots(QQbar, multiplicities = false)
mult = [d(P) for P in roots]
mult = [mult[k] for k in [0,1,2,3,6,8,9,10,11,18,20,21,42,43]]
v = [0..len(mult)-1]
spv = 0
S = Set(v)
SB = Subsets(S,type)
for subset in SB:
prod = 1
for k in range(0,len(subset)):
prod = prod * mult[subset[k]]
spv = spv + prod
ComplexField(100)(spv)
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