[Seqfan] Re: [Seqfan] Re: Need some help from Fibonacci experts...

[Thomas Baruchel]

On Sat, Jul 30, 2005 at 11:10:52AM +0200, Ralf Stephan wrote:
> But this may not help if you want solutions at once. Rather, if you
> are of the pragmatic type, you should read about the LLL algorithm,
> because generating functions are used only for finding which sort of
> solution is possible, not the actual solution.

I got that point, and I already started to read. I am also interested
by the theory, not only the practical point of view. Actually, I
already know LLL. I started to implement Maxima functions for
getting an ogf of the kind P(x)/Q(x) where P and Q are both
polynomials. But I wonder how you do that :

  Knowing my function a(n), I can compute the ogf for values of z
  like 1/50, 1/51, 1/52, ... Then with continued fractions I can
  simplify the result in order to get the probable exact value
  of ogf(z) since the continued fraction expansion contains
  very high partial quotients. Then I have the values of z:
  [1/51,1/52,1/53,...]
  and the values of ogf(z):
  [51/2549,52/2651,53/2755,...]    Here, a(n) = fibonacci(n)
  Now, how can I get P(x)/Q(x) if I suspect them to be polynomials
  (which seems to be the case for the functions I use) ? Ie. how
  did you get yourself to find the ogf of my functions from this
  last step ?

Regards,

-- 
Thomas Baruchel