Re: surrogate factoring

Thanks.

If you are really interested, the best way probably is asking him in a
polite manner directly instead of the public.

Have you ever tried that? I haven't once seen any evidence that a
direct question to JSH is the 'best way'.


Ulrich Diez wrote:
gjedwards@xxxxxxxxx wrote:

The bit I don't get (well one of the bits) is what specifically JH
*thinks* is the point of surrogate factoring. I know it's total
nonsense but does anyone have a clue *why* he thinks it's worthwhile?

Sorry, but I don't have my remote-mind-scanner available right now.
How shall we know why another person thinks what s/he thinks?
If you are really interested, the best way probably is asking him in a
polite manner directly instead of the public.

A reason for thinking that something is worthwhile might be that at
first glimpse it looks promising. In order to get why "surrogate factoring"
might look promising at first glimpse, you need to get the concept.
(I think at second glimpse "surrogate factoring" does not look all too
promising any more.)

I *think* you don't want to know why JH thinks it's worthwhile but you
want somebody to explain it to you so that you can judge upon
worthwhileness yourself.

I *think* the concept is:

Assume you want to factor a known integral target-number
"T" into 2 yet unknown integral factors. In other words:
You want to find integral "g_1" and "g_2" so that:
T = g_1 * g_2.

Furthermore assume that you have another known integer
"I" with already _known_ integral factors "f_1" and "f_2":
I = f_1 * f_2.

As I and T are known, the difference I - T = k is also a
known integer.

So you get the equation

f_1 * f_2 = k + g_1 * g_2

,where f_1 and f_2 and k are known integers and you want
to solve for integral g_1, g_2 which are factors of T.

I *think* JH observed that if

I) f_1 is of pattern w + x - 2z and
II) f_2 is of pattern w + 3x + 2y + 2z and
III) k is of pattern 2x^2 + 2xy + y^2 - 2w^2 - z^2 - 2xz and
IV) g_1 is of pattern w + x + y + z and
V) g_2 is of pattern 3w + x - y - 3z

, the above equation yields a true expression.

I *think* his idea is:

f_1, f_2 and k are known.

So find solutions w,x,y,z to the system formed by I) II) and
III)

I) f_1 = w + x - 2z
II) f_2 = w + 3x + 2y + 2z
III) k = 2x^2 + 2xy + y^2 - 2w^2 - z^2 - 2xz,

and use these solutions for calculating g_1 according to IV)
and g_2 according to V).

Solving this system would be the actual task.

Now I thought a lot while I consider thinking also a
matter of luck/brain-gambling.

Now one could waste time thinking about the following
questions:

- Will any solution w,x,y,z to the system I) II) III)
deliver integral g_1 and integral g_2?
Or will you just get a bunch of solutions and still
need to select appropriate-ones?

- From integral f_1, f_2 and k, you want to find
integral g_1, g_2.
If you find an all-integral solution w,x,y,z to the
system I) II) III), g_1 and g_2 will of course be
integers also.
But:
In order to get f_1, f_2, k, g_1, g_2 all integral, is
it really a requirement for w,x,y,z to be all integral
also? Is only considering diophantic-solutions w,x,y,z
sufficient?

This is no longer funny.

Ulrich

.