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Search: Posts Made By: Peter Hackman
Forum: Factoring 2009-10-26, 13:43
Replies: 7
Views: 1,357
Posted By Peter Hackman
Thanks. I've ordered the article from my old...

Thanks. I've ordered the article from my old university, but haven't received it yet. I suppose that sieveing is not exact (logarithms? ignoring small primes?), meaning at least some trial division,...
Forum: Factoring 2009-10-19, 13:52
Replies: 7
Views: 1,357
Posted By Peter Hackman
Algorithm 6.4.1 in Crandall-Pomerance. The field...

Algorithm 6.4.1 in Crandall-Pomerance. The field is Z/<p>.
Forum: Factoring 2009-10-19, 08:54
Replies: 7
Views: 1,357
Posted By Peter Hackman
trial division over a factor base

Not sure this is the right forum - if not, perhaps the moderator can move the thread.

I am trying to implement the Index Calculus algorithm for discrete logarithms. My program seems to work, but...
Forum: Math 2008-09-24, 16:34
Replies: 4
Views: 778
Posted By Peter Hackman
Don't know really what I meant to say in the...

Don't know really what I meant to say in the last sentence. There are 8 solutions.
Forum: Math 2008-09-24, 11:54
Replies: 4
Views: 778
Posted By Peter Hackman
Thanks for the links. Seems I will have to check...

Thanks for the links. Seems I will have to check the references more colsely to find out about the math side of it. The programming part sems to be amply documented. The (naive) Python routine given...
Forum: Homework Help 2008-09-24, 10:51
Replies: 8
Views: 2,526
Posted By Peter Hackman
Sorry: ...

Sorry:

http://www.mai.liu.se/~pehac/kurser/TATM54/booktot.pdf
Forum: Homework Help 2008-09-24, 10:22
Replies: 8
Views: 2,526
Posted By Peter Hackman
I suppose it's too late for your purposes, but...

I suppose it's too late for your purposes, but then I'm not breaking
the rules.

I'm surprised no one has answered your question. It's a standard result
in Elementary Number Theory and its proof...
Forum: Math 2008-09-19, 06:39
Replies: 4
Views: 778
Posted By Peter Hackman
N queens on an N/N board.

I recently ran a simple program for the N queens problem. 12 queens took minutes, 13 queens took hours, and beyond that I need a couple of friends.
Finding the number of orbits under the full...
Forum: Factoring 2008-08-15, 14:26
Replies: 2
Views: 3,237
Posted By Peter Hackman
Perhaps the example below helps clarify my...

Perhaps the example below helps clarify my observations/questions.
I've run it with varying small primes bounds (but always the same tolerance term, 2*int(log(pmax))
and factor base sizes. In my...
Forum: Factoring 2008-08-14, 07:02
Replies: 2
Views: 3,237
Posted By Peter Hackman
lots of large primes

I going over my QS hobby programs I've been running two versions, one with multipliers, one without.

Typically my runs have been on 50-digit numbers (as I've indicated elsewhere my Python...
Forum: Factoring 2008-08-12, 15:45
Replies: 13
Views: 883
Posted By Peter Hackman
Preferred languages?

After a period of devoting my energy to non-mathematical interests I recently looked over my programs, including a simple MPQS, an even simpler ECM (I took stage 2 from Crandall-Pomerance), and a...
Forum: Homework Help 2008-08-06, 19:17
Replies: 10
Views: 4,130
Posted By Peter Hackman
Suppose E is a subfield of F, with p^n and p^m...

Suppose E is a subfield of F, with p^n and p^m elements, respectively.
Let d denote the dimension of F as a vector space over E, and let B be a basis.
There are (p^n)^d linear combinations of B,...
Forum: Math 2007-11-17, 10:01
Replies: 2
Views: 426
Posted By Peter Hackman
And, of course, the problem is perfectly trivial...

And, of course, the problem is perfectly trivial if you replace all right members by -1.
Forum: Math 2007-11-17, 05:10
Replies: 2
Views: 426
Posted By Peter Hackman
They arrived at the soultion by a horrible...

They arrived at the soultion by a horrible mistake.

The solution form suggested assumes that the moduli are relatively prime in pairs; however, (4,6)=2. (And 2 divides 5-3=2, so the data are...
Forum: Factoring 2007-11-02, 15:59
Replies: 36
Views: 4,102
Posted By Peter Hackman
Thanks for you response. I'm aware of some of the...

Thanks for you response. I'm aware of some of the shortcomings of Python
in this context; for instance, binary Euclid is much slower than the division variant at that level! I never extended it.
...
Forum: Factoring 2007-10-28, 14:52
Replies: 36
Views: 4,102
Posted By Peter Hackman
I ran the program simply because I have it. It...

I ran the program simply because I have it. It (my version) is not fast; I think this factorization took 3 seconds.

Im impressed with the running times that people give here. I'm a pure...
Forum: Factoring 2007-10-27, 20:23
Replies: 36
Views: 4,102
Posted By Peter Hackman
Unless my programs are completely wrong, this...

Unless my programs are completely wrong,
this number yields completely to Pollard rho; the largest prime factor (38 digits) can be certified by elementary means (Pratt)!
Forum: Math 2007-10-22, 15:09
Replies: 2
Views: 553
Posted By Peter Hackman
primtive roots mod p^2

p=40487 is a prime number, 5 is its least positive primitve root. It is not a primitive root modulo p^2 (the least primtive root mod p^2 is 10).

p is the smallest odd prime having this property....
Forum: Factoring 2007-10-17, 10:30
Replies: 0
Views: 240
Posted By Peter Hackman
QS - reflections and questions

I haven't had the time to browse this forum so I apologize if my observations and questions are elsewhere to be found. I'll be grateful for a pointer.

Lately I've been toying with a simplified...
Forum: Factoring 2007-10-17, 08:56
Replies: 39
Views: 2,568
Posted By Peter Hackman
Short introduction: I'm new here. I'm a former...

Short introduction: I'm new here. I'm a former lecturer at Linköping University; took early retirement last year. Computational Number Theory is not my specialty (my field is Commutative Algebra)...
Showing results 1 to 20 of 20

 
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