Re: JSH: SF: Finally, surrogate factoring



Tim Peters wrote:
[Rick Decker]


<snip>


[jstevh@xxxxxxx]

<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.

<snip enough so that this subthread is completely unreadable
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 *** :-)

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

instead.

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

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