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 Showing results 1 to 20 of 20 Search took 0.01 seconds. Search: Posts Made By: Peter Hackman
 Forum: Factoring 2009-10-26, 13:43 Replies: 7 Views: 1,300 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: 1,300 Posted By Peter Hackman Algorithm 6.4.1 in Crandall-Pomerance. The field... Algorithm 6.4.1 in Crandall-Pomerance. The field is Z/

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 Forum: Factoring 2009-10-19, 08:54 Replies: 7 Views: 1,300 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: 756 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: 756 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: 2,269 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: 2,269 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: 756 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: 3,174 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: 3,174 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: 861 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: 4,032 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: 416 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: 416 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: 4,058 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: 4,058 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: 4,058 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: 533 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: 238 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: 2,547 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)...
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