Hi Raouf,
Sorry it's taken so long for someone to really try out your code. I
changed a few bits around, and tried to speed things up -- but I
wasn't sure exactly what certain parts of your code were supposed to
do, since several variables were undefined (such as "n").
What is this code trying to calculate?
Here's a slightly different version of your code:
borneSup=103196184763
S=0
Bm=0
alpha=1
p=2
m1=2
x=PolynomialRing(QQ,'x').gen()
f = gen_laguerre(2,1,x)
f_fast = f._fast_float_()
while (p^alpha) <=borneSup:
while (p^alpha) <=borneSup:
m1=p^alpha
if gcd(m1,6)==1:
mangoldt = RDF(p).log() / (RDF(m1)**(1.5))
j = RDF(m1).log()
Lg = f_fast(j)
M = ModularSymbols(6,2)
if gcd(p,6)==1:
if alpha ==1:
T1 = M.hecke_operator(p)
Bm=T1.trace()
if alpha>=2:
T1 = M.hecke_operator(p^alpha)
trace1=T1.trace()
T2 = M.hecke_operator(p^(alpha-2))
trace2=T2.trace()
Bm=trace1-((p)*trace2)
S=S+(mangoldt*Bm*Lg)
alpha=alpha + 1
Bm=0
alpha=1
p=next_prime(p)
print "S=",float(S)
However, this code also has no chance of completing. If you replace
borneSup with the first half of its digits, i.e. 10319, this code will
run just fine. However, even if you make the bound 103196, this code
probably won't finish. You're asking it to compute some insanely large
number of Hecke operators on this space ... Also, the space you're
working with happens to consist solely of Eisenstein series -- is this
really the space you're interested in? If so, you could probably
compute this information another (faster) way.
In particular, it would help if you gave us a hint of what you were
trying to do ...
-cc
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