Text 35, 59 rader
Skriven 2004-08-03 15:37:05 av Jasen Betts (3:640/1042)
     Kommentar till text 19 av DAVID WILLIAMS (1:250/514)
Ärende: Pythagorean triples
===========================
Hello DAVID.

02 Aug 04 09:17, you wrote to me:

 DW> -> while b > 1
 DW> -> z= a mod b : a=b: b=z
 DW> -> wend
 DW> -> if b=1 then a=1

 DW> -> Jasen

 DW> So I take it that (in the mod code) the final value of a is the GCF?

yes.

 DW> I've tested it, and it does seem to work. I'll get around to figuring
 DW> out the logic!


it's probably more useful to consider the mod operator as a "remainder"
operatior in this context.

start with,   a=xm. b=ym is fairly easy to prove that iterating the while
results in reducing a (and b) to smaller values that are still multiples of m

 DW> So what I now have in the program is:

 DW> U = A
 DW> V = B
 DW> DO WHILE V > 1
 DW>   W = U MOD V
 DW>   U = V
 DW>   V = W
 DW> LOOP
 DW> IF U = 1 OR V = 1 THEN ... (A and B have no common factors > 1)

    if v then ....
 would be sufficient, U will never be 1 (unless A and B were both 1)
          in which case V will be 1

 DW> That's right, yes? It does seem to work just fine.

 DW> In a couple of messages, you have sounded puzzled about why there seem
 DW> to be two "families" of solutions to things. This is the reason. They
 DW> correspond to the above two cases.

yes... I figured that out after looking at your forulae,

Mail has been a bit sluggish but I think I've figured out why.

 DW> It's glorious summer weather here - not conducive to playing with
 DW> computers. But I will work on this some more sometime!

It's 25C in the shade here... and it's what they call winter.

Jasen

--- GoldED+/LNX 1.1.4.7
 * Origin:  (3:640/1042)