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

 Messages: [ Previous | Next ]
 Rick Decker Posts: 1,356 Registered: 12/6/04
Re: JSH: SF: Finally, surrogate factoring
Posted: Jun 7, 2006 10:29 PM

Tim Peters wrote:
> [Rick Decker]
>

<snip>
>
>
> [jstevh@msn.com]

<snip>
>>>
>>>But your solution has more than that because it gives
>>>
>>>y = (5f_1 - 3f_2 + 21g_1 - g_2)/4
>>>
>>>as a solution as well.

>
>
> [Rick Decker]
>

>>No. However, it would be interesting to see how you got this.

to anyone who hasn't been following closely>
>
> Are you psychic or what?

Yes, and I knew you'd ask that.

> I had no idea how he came up with the thing
> containing 21g_1, and never would have guessed he was just pulling it out of
> his butt :-)

Surely you're not surprised.
>
>

>>Let h_1 and h_2 be chosen so that h_1 * h_2 = 21 * T
>>
>> h_1 + h_2 = 10*y + 42*z + 19*f_1 - 3*f_2 [1]
>> h_2 - h_1 = 4*y - 5*f_1 + 3*f_2 [2]

>
>
> I think you meant to write h_1 - h_2 on the LHS of [2].

Indeed I did.
>
>

>>Then we can write
>>
>> (10*y + 42*z + 19*f_1 - 3*f_2)^2 = (4*y - 5*f_1 + 3*f_2)^2 + 84*T
>>
>>in the form
>>
>> (h_1 + h_2)^2 = (h_1 - h_2)^2 + 4 * h_1 * h_2

>
>
> This part would be clearer with the correction above.

Yes.
>
>

>>Then, from [1] and [2] we solve for y to get
>>
>> y = (5*f_1 - 3*f_2 + h_1 - h_2) / 4 [3]

>
>
> While this conclusion _needs_ the correction above.

Yes, yes.
>
>

>>Then, since h_1 * h_2 = 21 * T = 21 * g_1 * g_2 we may as well
>>pick h_1 = 21 * g_1 and h_2 = g_2 so [3] becomes
>>
>> y = (5*f_1 - 3*f_2 + 21*g_1 - g_2) / 4
>>
>>Right?

>
>
> Yes, you are psychic!

I knew you'd say that.
>
>

>>If that was your reasoning, it's wrong. You can't pick any old
>>values for h_1 and h_2. Watch:
>>
>>Solving [1] and [2] for h_1 and h_2 we get
>>
>> h_1 = 7(y + 3 * z + f_1)
>> h_2 = 3(y + 7 * z + 4 * f_1 - f_2)

>
>
> That also needs the correction above ;-)

(Grr). Yes, yes, yes!
>
>

>>But from your original four linear equations we can derive
>>
>> g_1 = y + 3 * z + f_1
>> g_2 = y + 7 * z + 4 * f_1 - f_2
>>
>>in other words, we are forced to choose
>>
>> h_1 = 7 * g_1
>> h_2 = 3 * g_2
>>
>>and not your h_1 = 21 * g_1 and h_2 = g_2.

>
>
> And to force the conclusion, in that case [3] becomes
>
> y = (5*f_1 - 3*f_2 + 7*g_1 - 3*g_2)/4
>
>
> But let's give James something else to worry about :-) Take
>
> (42*z + 10*y - 3*f_2 + 19*f_1)^2 = (4*y + 3*f_2 - 5*f_1)^2 + 84*T
>
> expand it, use the quadratic equation to solve for y, and then substitute to
> get rid of z and T:
>
> z = -(3*f_1 - f_2 + g_1 - g_2)/4
> T = g_1*g_2
>
> The result is:
>
> y = (5*f_1 - 3*f_2 + 5*g_1 - 5*g_2 +/- 2*(g_1 + g_2))/4
>
> Pick "+" and you get the result James wants:
>
> y = (5*f_1 - 3*f_2 + 7*g_1 - 3*g_2)/4
>
> Pick "-" and it's different:
>
> y = (5*f_1 - 3*f_2 + 3*g_1 - 7*g_2)/4
>
> Woo hoo! Centuries of mathematics down the tubes again, or can James spot
> the bogosity? Hint #1: this isn't an algebraic error; you really do get
> that result for y. Hint #2: you get the same two results for y if you do
> the same thing but starting from
>
> (2*y + 10*z + 5*f_1 - f_2)^2 = (4*z + 3*f_1 - f_2)^2 + 4*T
>

Hehe. I predict that this section (cute, BTW) will generate no response.
>
>

>><snip>

>>>I wonder if you just lied.
>
>

>>You just can't resist, can you? Are you naturally boorish, or do
>>you have to work at it?

>
>
> I strongly suspect that bit of gratuitous assholishness was deliberate. God
> only knows why, but James got it into his head that he needs to _provoke_
> people into replying when he thinks they know something he wants to find
> out. That's just his despicable way of trying to goad you into doing his
> work for him. It's especially idiotic in this case, since if he had any
> memory he'd recall that you typically respond much better to polite requests
> than to his stupid baiting tactics.
>
> But, in this case, I'm afraid what he'll take away is "ha! it worked again",
> without a shadow of a clue that it was neither necessary nor helpful to
> behave like an ass.
>

Sadly, I predict you're right again.

Regards,

Rick

Date Subject Author
6/4/06 JAMES HARRIS
6/5/06 Doug Schwarz
6/5/06 Tim Peters
6/5/06 Doug Schwarz
6/5/06 Christopher J. Henrich
6/5/06 Gib Bogle
6/5/06 Proginoskes
6/5/06 William L. Bahn
6/5/06 JAMES HARRIS
6/5/06 Abstract Dissonance
6/5/06 Abstract Dissonance
6/5/06 Salami Man
6/5/06 William L. Bahn
6/6/06 Brian Quincy Hutchings
6/5/06 guenther.vonKnakspott@gmx.de
6/6/06 Matthijs Hebly
6/6/06 Salami Man
6/5/06 Abstract Dissonance
6/5/06 Gordon Burditt
6/5/06 Sebastian Gottschalk
6/5/06 dkguru
6/5/06 Ed Weir \(ComCast\)
6/5/06 Abstract Dissonance
6/5/06 Andrew Swallow
6/5/06 gjedwards@gmail.com
6/5/06 Salami Man
6/5/06 Gib Bogle
6/6/06 TC
6/6/06 Salami Man
6/5/06 Sebastian Gottschalk
6/5/06 JAMES HARRIS
6/5/06 marc.t.davies@gmail.com
6/5/06 gjedwards@gmail.com
6/5/06 LarryLard
6/5/06 William L. Bahn
6/5/06 Richard Henry
6/5/06 Salami Man
6/5/06 Bob Marlow
6/5/06 Bob Marlow
6/5/06 none
6/5/06 rossum
6/5/06 Rick Decker
6/5/06 JAMES HARRIS
6/5/06 jshsucks@yahoo.com
6/5/06 Salami Man
6/5/06 Tim Peters
6/5/06 JAMES HARRIS
6/5/06 Tim Peters
6/6/06 Rick Decker
6/6/06 Rick Decker
6/6/06 Tim Peters
6/6/06 Rick Decker
6/7/06 David C. Ullrich
6/7/06 Rick Decker
6/7/06 Jesse F. Hughes
6/7/06 Rick Decker
6/8/06 David C. Ullrich
6/7/06 Bertie Reed
6/6/06 JAMES HARRIS
6/6/06 JAMES HARRIS
6/7/06 Rick Decker
6/7/06 Tim Peters
6/7/06 Rick Decker
6/8/06 JAMES HARRIS
6/8/06 Jose Carlos Santos
6/8/06 Rick Decker
6/8/06 LarryLard
6/8/06 David Bernier
6/8/06 Rick Decker
6/9/06 Tim Peters
6/9/06 david250@gmail.com
6/9/06 marcus_b
6/8/06 Richard Henry
6/8/06 jshsucks@yahoo.com
6/8/06 Paul Sperry
6/8/06 LarryLard
6/8/06 Denis Feldmann
6/8/06 David Bernier
6/8/06 David C. Ullrich
6/8/06 David Moran
6/8/06 David Bernier
6/8/06 Tim Peters
6/8/06 Proginoskes
6/10/06 Tim Peters
6/10/06 Tim Peters
6/6/06 gjedwards@gmail.com
6/6/06 Proginoskes