# Compiling .spyx-files

This is an implementation of the pollard-rho factorization-algorithm in sage (filename: exp.sage)

def pollard_rho(n):
x = 2
y = x
t = 1

while t == 1:
x = mod(x,n)^2+1
y = mod(mod(y,n)^2+1,n)^2+1
t = gcd(x-y,n)

if t<n:
return(t)
else:
return 0

But trying to compile

import sage.all

def pollard_rho(n):
x = 2
y = x
t = 1

while t == 1:
x = sage.all.mod(x,n)**2+1
y = sage.all.mod(sage.all.mod(y,n)**2+1,n)**2+1
t = sage.all.gcd(x-y,n)

if t<n:
return(t)
else:
return 0

named as "exp.spyx" brings several errors, one of them (f.e.):

13     while t == 1:
14       x = sage.all.mod(x,n)**2+1
---> 15       y = sage.all.mod(sage.mod(y,n)**2+1,n)**2+1
16       t = sage.all.gcd(x-y,n)
17

AttributeError: 'module' object has no attribute 'mod'

What is wrong here? Probably many things - im totally new to Sage, coming from Pari-gp and work in console-mode - no experiences with C or Python. Thank you.

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I think the version you tried to compile is different than the one posted above. In the error message, you can see the line sage.all.mod(sage.mod(y,n)**2+1,n)**2+1 which includes sage.mod which doesn't appear anywhere in the version you posted.

When I try to compile the exp.spyx file posted above, then everything works fine for me. Try that and let me know how it goes.

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Yes, sorry, thank you Mike and DSM - it seems as if I intended to annoy people here with this. I did correct that in my posting, but didn't realize that this could be the mistake ... To be sure: On my machine theres absolutely no speed-up of the compiled version (its even a bit slower), whys that?

( 2011-01-08 11:07:17 +0200 )edit

It seems to work for me:

Compiling exp.spyx...
sage: time pollard_rho(next_prime(10**6)*previous_prime(10**7))
CPU times: user 0.23 s, sys: 0.01 s, total: 0.23 s
Wall time: 0.24 s
1000003

I'm a little puzzled, though, because the error message you show doesn't seem to correspond to the line in your source, namely that in the code you put up it says "sage.all.mod(sage.all.mod(y,n)**2+1,n)**2+1" but the error message points to a line of code reading "y = sage.all.mod(sage.mod(y,n)**2+1,n)**2+1", without an ".all." between sage and mod, so it seems to be looking in the module "sage" for the function mod.

For what it's worth, that's exactly the error message I get if I remove the ".all".

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