Hi Ralf!
R> there is no need for taylor() (Maxima)
R> if you use series() (Pynac) which is way faster.
I cannot reproduce your claim, in the contrary.
Please consider this simple example:
def num(m, n, ser):
z = var('z')
w = exp(2 * pi * I / m)
o = sum(exp(z * w^k) for k in range(m)) / m
f = 1 / o
if ser:
t = f.series(z, n + 1)
else:
t = taylor(f, z, 0, n + 1)
return factorial(n) * t.coefficient(z, n)
ser = lambda m,n: sum(binomial(m*n,m*k)*num(m,m*k,true )*k/n for k in
(1..n))
tay = lambda m,n: sum(binomial(m*n,m*k)*num(m,m*k,false)*k/n for k in
(1..n))
---
import time
print time.clock()
print [[tay(m,n) for n in (1..6)] for m in (1..5)]
print time.clock()
print [[ser(m,n) for n in (1..6)] for m in (1..5)]
print time.clock()
In fact if I would not have killed the program I think
the series version would still run.
If I have misunderstood, please do enlighten me.
Peter
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