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Forum: Math 2017-07-25, 10:21
Replies: 6
Views: 788
Posted By paul0
I stand corrected. Thanks for clarifying :)

I stand corrected. Thanks for clarifying :)
Forum: Math 2017-07-25, 09:10
Replies: 6
Views: 788
Posted By paul0
I think you misunderstood. Instead of solving the...

I think you misunderstood. Instead of solving the probability of smoothness, I want to solve for X given B and the probability.
Forum: Math 2017-07-24, 12:24
Replies: 6
Views: 788
Posted By paul0
Inverse of Smoothness Probability

The probability that a random number below X is B-smooth is given by u-u, where u=ln(X)/ln(B). However, I would like the do the inverse, that is, given the smoothness probability and B, how do I...
Forum: Factoring 2015-11-20, 21:12
Replies: 6
Views: 983
Posted By paul0
I'll research about all of those and implement...

I'll research about all of those and implement them eventually. I'll probably abandon the python lattice siever and move to C since I can control lots things there, like the sieve and factor base...
Forum: Factoring 2015-11-18, 20:43
Replies: 6
Views: 983
Posted By paul0
In gnfs-lasieve, why is there two parameters (for...

In gnfs-lasieve, why is there two parameters (for rational and algebraic) for the sieving bound? Is the sieve checked twice? If so, what is the advantage instead just checking it once? The sieve adds...
Forum: Factoring 2015-11-18, 14:00
Replies: 6
Views: 983
Posted By paul0
I was reading Franke's siever's readme, it uses...

I was reading Franke's siever's readme, it uses this as bound: log(abs(polynomial value))-lambda*log(factor base bound)

As for I and J, I think I have to experiment to find good values, as I doubt...
Forum: Factoring 2015-11-18, 13:58
Replies: 5
Views: 731
Posted By paul0
I like to point out that for now, my NFS...

I like to point out that for now, my NFS implementation is a learning (toy) experiment. It won't be made to compete.
Forum: Factoring 2015-11-18, 06:16
Replies: 5
Views: 574
Posted By paul0
No particular reason, python 2 is what I...

No particular reason, python 2 is what I currently have installed. I'll switch to python 3 soon.



if anyone's looking, I renamed the file:...
Forum: Factoring 2015-11-17, 22:06
Replies: 6
Views: 983
Posted By paul0
Lattice Sieving Parameters

Now that I can generate a sublattice basis and reduce it, I think I'm ready to write a lattice siever. However, there seems to be more parameters I don't know how to set:
1) the sieving region I and...
Forum: Factoring 2015-11-17, 14:47
Replies: 5
Views: 574
Posted By paul0
It appears that I was confusing the rows &...

It appears that I was confusing the rows & columns of the matrix, I was running it like this in Pari:


(22:53) gp > x = [-110, 1;249, 1]
%15 =
[-110 1]
[ 249 1]

(22:53) gp > x=x*qflll(x)...
Forum: Factoring 2015-11-17, 13:39
Replies: 5
Views: 574
Posted By paul0
Generating reduced basis for special-q

Hello,

I have code that tries to generate lattice points of a special-q: https://github.com/paulocode/ppyNFS/blob/master/specialq-lattice.py

However, norms of points it generates through the...
Forum: Programming 2015-11-17, 13:04
Replies: 2
Views: 1,304
Posted By paul0
Thank you :)

Thank you :)
Forum: Programming 2015-11-17, 12:35
Replies: 2
Views: 1,304
Posted By paul0
LLL in GP/Pari

I'm trying the qflll function Pari for lattice reduction. However, I'm not getting correct answers.

First, the wikipedia example:...
Forum: Factoring 2015-11-16, 16:11
Replies: 5
Views: 731
Posted By paul0
Oh, I was assuming that the two sides are sieved...

Oh, I was assuming that the two sides are sieved separately, as in two different memory allocations, producing two different sets of smooth pairs. It's clearer to me now. Thanks.
Forum: Factoring 2015-11-16, 15:24
Replies: 5
Views: 731
Posted By paul0
So there is an implicit "match the smooth pairs...

So there is an implicit "match the smooth pairs from both sides" step?
Forum: Factoring 2015-11-16, 14:53
Replies: 5
Views: 731
Posted By paul0
Sieving both sides vs one side at a time

My line siever currently sieves N(a+bθ)*(a+bm), which is the algebraic side and the rational side at the same time. However, it looks like most papers point to sieving the two sides separately. What...
Forum: Factoring 2015-11-16, 14:17
Replies: 7
Views: 1,064
Posted By paul0
may I have a copy of your Java implementation?

may I have a copy of your Java implementation?
Forum: Factoring 2015-11-15, 14:02
Replies: 7
Views: 1,064
Posted By paul0
Block Wiedemann for beginners

Hello, I'm trying to implement a faster LA step instead my current Gaussian Reduction implementation. As what usually happens with new concepts, I can't comprehend how Block Wiedemann works. I think...
Forum: Factoring 2015-03-31, 10:48
Replies: 4
Views: 854
Posted By paul0
I used the recursive "random splitting" algorithm...

I used the recursive "random splitting" algorithm as described in page 103 of Prime Numbers: A Computational Perspective. See functions getRootsModPFast() and getRootsModPSlow() in poly.py.

...
Forum: Factoring 2015-03-29, 21:06
Replies: 4
Views: 854
Posted By paul0
ppyNFS

Hi guys,

I've been asking lots of questions here to understand NFS, and people who answered really helped me understand it. So, I was able to eventually code NFS, it's a really good learning...
Forum: Factoring 2015-03-14, 19:55
Replies: 3
Views: 914
Posted By paul0
Still playing around with this... An actual...

Still playing around with this...

An actual factorization choose (4+i) and (8+19i) as relations form a square since:
(4+m)*(8+19m) = 2102
(4+i)*(8+19i) = 13+84i = (7+6i)2

So, (7+6i)2 and...
Forum: Factoring 2015-03-14, 00:18
Replies: 3
Views: 914
Posted By paul0
Consider f(x) = x2 + 1, m=46, n=2117 let β =...

Consider f(x) = x2 + 1, m=46, n=2117
let β = -11+3i.
φ(-11+3i) = -11+3*46 = 127 mod 2117
Using the homomorphism and factoring -11+3i in different ways, we can generate many more numbers that are...
Forum: Factoring 2015-03-13, 19:14
Replies: 3
Views: 914
Posted By paul0
Some ideas regarding NFS...

If the ring produced by NFS is not a UFD, then the square produced in the ring can be factored in different ways. I was thinking, is it possible to use these different factorizations to produce...
Forum: NFS@Home 2015-03-12, 19:11
Replies: 2
Views: 983
Posted By paul0
What exactly is sent to the server?

Is it the floating point results of the sieve area from adding log(p), or the smooth (a,b) pairs? Also, is there a way get more information on what's exactly going on in lasieve, like a log output?
Forum: Factoring 2015-03-08, 21:52
Replies: 3
Views: 1,135
Posted By paul0
Lattice Sieving - where do I start?

My python NFS implementation is now up and working, and mostly cleaned. I currently use line sieving, now I want to take it up a notch with lattice sieving. But where do I start? Is there an explicit...
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