Integer factorization, etc.
in [Math]
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From: David Bernier on 15 Apr 2008 13:34 Pubkeybreaker wrote: > On Apr 14, 10:21 am, Pubkeybreaker<pubkeybrea...(a)aol.com> wrote: >> On Apr 12, 6:07 am, David Bernier<david...(a)videotron.ca> wrote: >> >>> Marshall wrote: >>>> On Apr 11, 6:49 pm, Tim Smith<reply_in_gr...(a)mouse-potato.com> wrote: >>>>>> [...] has a record of not suffering fools easily. [....] >>>>> None of the above, though, is inconsistent with being a jerk. >>>> Every time I have ever seen the phrase "not suffer fools gladly," >>>> it has been an apologist acknowledgment of a respected person's >>>> bad behavior. It's a code phrase used to describe high >>>> status jerks. >>> I think it's always used by someone referring to another person's >>> way of dealing with "fools". I would think that there's generally >>> an implied context, such as " when the topic is algorithms used >>> in number theory" . How often is it said on TV? >> You will notice that nothing I said included name calling such as >> "jerk". >> Nor did I call the OP a "fool". >> >> Indeed, I went out of my way to state that I intended no insult toward >> the >> OP. Stating that someone lacks knowledge is not and should not be >> consisidered an insult or ad hominem attack. It is a simple >> statement >> of fact. Ignorance is easily corrected, unless it is WILLFUL >> ignorance. >> In which case, the person deserves to be called a crank. >> >> I did not even call the OP a crank. I did say that some of his >> discussion indicated crank-like behavior. >> >> I get the impression that some people who post herein believe that >> any criticism of the work of another constitutes "jerk-like" behavior. >> >> Note also that Dik Winter also replied to the OP, and that the OP's >> response >> was to become argumentative with someone (Dik) who knows far more >> about the subject than the OP. >> >> When the OP started talking about "square roots", all I did was to >> state >> that it was an elementary and well-solved problem. >> >> When someone else asked about factoring Gaussians, I simply stated >> an algorithm. >> >> When the OP talked about his "new" method using Gaussian integers as >> a new way of looking at Fermat's method, I pointed out that they were >> P-time equivalent. > > No comments? Well, I've read pretty much (or at least browsed) the whole thread from the very beginning at the Google archives. There have been many back-and-forth replies between you and Risto. It's what I would call a big tiff or a major run-in, probably with bad feelings on both parts. If I felt like trying to analyze it further, then I would. But I have more pleasant things to do, and I don't feel like analyzing the thread further, so I won't. From reading the thread, nothing shows that either of you is a bad person. Arguments that turn sour are a part of human nature. Compared to the political power struggle currently going on in Zimbabwe, there's nothing to worry about. In the post to which you reply above, I was unaware of the import of Marshall's post; I dissociate myself from Marshall's opinion. I point out that I put *fools* in scare quotes because I wanted to. My reply to Marshall was my take on the usage of the expression "doesn't suffer fools gladly", as those who read alt.usage.english might be inclined to do, i.e. finding out the subtle nuances from usage in books, newspapers, magazines and so on. I was curious about usage, and that's why I wrote: `` How often is it said on TV?". Had I known about the context, then I would have replied differently to Marshall, because he wrote "high status jerks", and given the way the thread went, in my view, "jerk" or "jerk behavior" doesn't apply to you. David Bernier
From: fortune.bruce on 15 Apr 2008 14:57 On Apr 15, 9:11 am, Nick Wedd <n...(a)maproom.co.uk> wrote: > In message > <2104b4ed-b84a-4c54-9309-15191ca8a...(a)x41g2000hsb.googlegroups.com>, > Pubkeybreaker <pubkeybrea...(a)aol.com> writes > > > > >On Apr 14, 10:21 am, Pubkeybreaker <pubkeybrea...(a)aol.com> wrote: > >> On Apr 12, 6:07 am, David Bernier <david...(a)videotron.ca> wrote: > > >> > Marshall wrote: > >> > > On Apr 11, 6:49 pm, Tim Smith<reply_in_gr...(a)mouse-potato.com> wrote: > >> > >>> [...] has a record of not suffering fools easily. [....] > >> > >> None of the above, though, is inconsistent with being a jerk. > > >> > > Every time I have ever seen the phrase "not suffer fools gladly," > >> > > it has been an apologist acknowledgment of a respected person's > >> > > bad behavior. It's a code phrase used to describe high > >> > > status jerks. > > >> > I think it's always used by someone referring to another person's > >> > way of dealing with "fools". I would think that there's generally > >> > an implied context, such as " when the topic is algorithms used > >> > in number theory" . How often is it said on TV? > > >> You will notice that nothing I said included name calling such as > >> "jerk". > >> Nor did I call the OP a "fool". > > >> Indeed, I went out of my way to state that I intended no insult toward > >> the > >> OP. Stating that someone lacks knowledge is not and should not be > >> consisidered an insult or ad hominem attack. It is a simple > >> statement > >> of fact. Ignorance is easily corrected, unless it is WILLFUL > >> ignorance. > >> In which case, the person deserves to be called a crank. > > >> I did not even call the OP a crank. I did say that some of his > >> discussion indicated crank-like behavior. > > >> I get the impression that some people who post herein believe that > >> any criticism of the work of another constitutes "jerk-like" behavior. > > >> Note also that Dik Winter also replied to the OP, and that the OP's > >> response > >> was to become argumentative with someone (Dik) who knows far more > >> about the subject than the OP. > > >> When the OP started talking about "square roots", all I did was to > >> state > >> that it was an elementary and well-solved problem. > > >> When someone else asked about factoring Gaussians, I simply stated > >> an algorithm. > > >> When the OP talked about his "new" method using Gaussian integers as > >> a new way of looking at Fermat's method, I pointed out that they were > >> P-time equivalent. > > >No comments? > > I don't know whose comments you want. > > When you accused the OP of writing "pure gibberish", I thought it a bit > harsh, his statement "Fermat's factorization suffers a fixation to > integers" appeared to me to have some meaning, which I attempted to > explain (the OP then disowned my explanation). You responded with a > full and clear explanation of how to factorise Gaussian integers, which > impressed me; I learned from it, and I thought "this guy knows his > stuff, I'll keep out of the argument". > > I don't understand why this thread has evolved into an argument about > posting behaviour. I would be willing to bet that those who have > criticised your posting style know less about factorisation than the > other contributors to the thread. I hope that you will continue to post > to this newsgroup. > > Nick > -- > Nick Wedd n...(a)maproom.co.uk Nick, you've summed up the issue fairly completely. A lot of us are here to learn and we are damn lucky to have persons like Bob Silverman (Pubkeybreaker) and Dik T. Winter willing to share their great knowledge. I think they deserve respect and a certain amount of leeway to get their point across and I think most of us who are not so precious as to be able to take a bit of hard critique, understand this. Like you, I would also be willing to bet that those who have criticized Pubkeybreaker's posting style know less about factorization than the other contributors to the thread. Bruce
From: Risto Lankinen on 15 Apr 2008 17:03 On 15 huhti, 17:34, Pubkeybreaker <pubkeybrea...(a)aol.com> wrote: > On Apr 14, 10:31 am, Pubkeybreaker <pubkeybrea...(a)aol.com> wrote: > > On Apr 12, 4:51 pm, Risto Lankinen <rlank...(a)gmail.com> wrote: > > > > No one for instance has > > > referred to prior art when it comes to my method. > > > This is false. Dik Winter told you that what you were doing > > was just a (disguised) form of Fermat's Method. This certainly > > IS a reference to prior art. > > No comments? I had already reasoned that arguing is futile, but you ask. I wasn't initially going to publish any algorithm; rather I was just asking whether anyone uses complex numbers (more precisely gaussian integers) in factoring. However, the C++ code I posted in one instance implements an algorithm whose purpose is to demonstrate the complex square root using factorization as an example (a very natural use for complex square root, IMO). Its asymptotic complexity is worse than that of trial multiplication, which should have either alerted an expert that the gist is elsewhere, or raise no interest at all. In any case, the algorithm scans line x=ki for points where N+ki is a square of a gaussian integer. Now, the book you pointed me to (Knuth Vol.2) describes Fermat's method thus: C1. x <- INT(2*SQRT(N))+1, y <- 1, r <- INT(SQRT(N))^2 C2. If r = 0 , done: N= ((x+y)/2) * ((x-y)/2) C3. r <- r+x, x <- x+2 C4. r <- r-y, y<-y+2 C5. If r > 0 go to C3 else go to C2 This is very similar to Bresenham's line and circle drawing algorithms but slightly adapted for drawing a hyperbole that crosses X-axis in SQRT(N) and approaches asymptitically both x=y and x=-y . Unlike Bresenham's, Fermat's algorithm terminates at the first instance where the tracking error is zero (i.e. when it hits an integer on both axis). And yet, I still fail to see the equivalence between the two. It is true that mathematically the hyperbole of Fermat's method is the track of the square root of a point travelling the line x=ki and they encounter divisors in the same order (though not rate), but if you allow such a leap between the two, then trial division should also become a member of the Fermat's method family because the only difference is that it tracks the hyperbole N = xy using exactly similar criteria, but travelling to the opposite direction. - - - Lesson learnt #1: In academia, the form is more important than the substance. I'll polish the puzzle formulation some day and post again, let's see what happens then. Lesson learnt #2: I stated I'm a layman, but that was a huge mistake. You and your followers thought "uneducated", when the intention was to communicate "self-educated". Respectfully, - Risto -
From: Risto Lankinen on 17 Apr 2008 16:22 On 16 huhti, 00:03, Risto Lankinen <rlank...(a)gmail.com> wrote: > On 15 huhti, 17:34, Pubkeybreaker <pubkeybrea...(a)aol.com> wrote: > > > On Apr 14, 10:31 am, Pubkeybreaker <pubkeybrea...(a)aol.com> wrote: > > > On Apr 12, 4:51 pm, Risto Lankinen <rlank...(a)gmail.com> wrote: > > > > > No one for instance has > > > > referred to prior art when it comes to my method. > > > > This is false. Dik Winter told you that what you were doing > > > was just a (disguised) form of Fermat's Method. This certainly > > > IS a reference to prior art. > > > No comments? I would be especially interested in comments from > > those who felt that I was being a "jerk". > > Lesson learnt #1: In academia, the form is more important > than the substance. No comments? I would be especially interested in comments from those who felt that I was exhibiting "hallmarks of a crank". - Risto -
From: Gerry Myerson on 17 Apr 2008 21:49
In article <d38c9367-f862-441d-a086-75d69b1d5b63(a)m44g2000hsc.googlegroups.com>, Risto Lankinen <rlankine(a)gmail.com> wrote: > On 16 huhti, 00:03, Risto Lankinen <rlank...(a)gmail.com> wrote: > > On 15 huhti, 17:34, Pubkeybreaker <pubkeybrea...(a)aol.com> wrote: > > > > > On Apr 14, 10:31�am, Pubkeybreaker <pubkeybrea...(a)aol.com> wrote: > > > > On Apr 12, 4:51�pm, Risto Lankinen <rlank...(a)gmail.com> wrote: > > > > > > > No one for instance has > > > > > referred to prior art when it comes to my method. > > > > > > This is false. �Dik Winter told you that what you were doing > > > > was just a (disguised) form of Fermat's Method. � This certainly > > > > IS a reference to prior art. > > > > > No comments? I would be especially interested in comments from > > > those who felt that I was being a "jerk". > > > > Lesson learnt #1: �In academia, the form is more important > > than the substance. > > No comments? I would be especially interested in > comments from those who felt that I was exhibiting > "hallmarks of a crank". Don't know about that, but if the #1 lesson you've learnt from sci.math, or from anywhere else, is that in academia the form is more important than the substance, then you haven't been paying attention. -- Gerry Myerson (gerry(a)maths.mq.edi.ai) (i -> u for email) |