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Topic:
SF: Finally, surrogate factoring
Replies:
86
Last Post:
Jun 10, 2006 11:51 PM




Re: JSH: SF: Finally, surrogate factoring
Posted:
Jun 6, 2006 8:54 PM


Tim Peters wrote: > [Rick Decker] > >>... >>So completing the square w.r.t y first yields >> >> (2*y + 10*z + 5*f_1  f_2)^2 = (4*z + 3*f_1  f_2)^2 + 4*T >> >>Completing the square w.r.t. z first yields >> >> (42*z + 10*y  3*f_2 + 19*f_1)^2 = (4*y + 3*f_2  5*f_1)^2 + 84*T >> >>and rewriting both these as differences of squares yields the same >>(useless) factorization of T: >> >> T = (y + 3*z + f_1)(y + 7*z + 4*f_1  f_2) > > > Macsyma agrees ;) > > >>and it's not hard to verify that >> >> g_1 = y + 3*z + f_1 >> >> g_2 = y + 7*z + 4*f_1  f_2 > > > Given that James started with (although it was obscured by the > presentation): > > f_1 = w + x  2*z > f_2 = w + 3*x + 2*y + 2*z > g_1 = w + x + y + z > g_2 = 3*w + x  y  3*z > > that's immediate. So, after small mountains of tedious manipulation, we get > back a minor respelling of the initial assumptions.
Of course. My observation was nothing more than a verification that all of this completingthesquare taradiddle was indeed correct (and, as you indicate below, trivial). Nice typesetting, BTW. > > What I don't understand is how anything other than that outcome could be > _hoped_ for here. No amount of rearranging and crosssubstituting the > initial equations (whatever they may be) is going to yield new information, > and there's never a step that even requires the quantities to be integers > (as opposed to, e.g., arbitrary complex numbers). How can someone imagine > that insight into integer factorization could result from this insightless > symbolpushing?
I think that what we interpret as obfuscation on James' part is actually a consequence of the fact that his understanding is extremely shallow. This is, I think, the reason that he thinks his "prime counting function" is truly new and innovativehe really is incapable of even the slightest bit of abstraction that to all mathematicians is as natural as breathing. > > As usual, I couldn't make sense of his original writeup before you showed > the correct result of completing the square wrt y first, at which point I > could work backward from that to deduce what you thought James was trying to > say. Also as usual, you got that right. Therefore :) you must also know > why he thinks this kind of approach _could_ yield something useful. > See above. The kind of selfediting we're accustomed to by inclination and training is something he simply doesn't get. For example, a tiny bit of thinking makes it obvious that no matter what collection of linear equations one starts with, as long as they have a unique solution the end result of the "small mountain of tedious manipulation" will be the completely unsurprising T = g_1 * g_1, which we knew from the start.
> Or is this another case where you know he's right, and are keeping silent > about which initial equations actually do work just to protect your career? > Clever, if so ;) > Clever you for deducing that. True, I've found that a simple modification of James' argument will allow one to factor N in log^2 (log N) steps, but I'm witholding it (a) to protect my career and (b) to crack all those RSA codes out there and make a bazillion bucks by theft, deceit, and blackmail.
Be afraid, be very afraid.
Regards,
Rick



