What are the PARI/GP alternatives to contfrac() ?

[Max Alekseyev]

On Dec 28, 2007 11:21 AM, Alexander Povolotsky <apovolot at gmail.com> wrote:

> I don't mind to be corrected but this time I just was quoting what the entry
> in the
> http://en.wikipedia.org/wiki/Continued_fraction wiki says.
> Perhaps you have not looked yourself at it directly
> (now I copied ant pasted it below for your viewing pleasure ).

Sure, I have.

> Max -  if you feel that discussed wiki entry incorrect - please do go ahead
> and correct it.

I have already corrected it.

> PS Could you please show your PARI/GP results in generating last two
> variants (as shown /pasted below) using contfrac() with additional argument
> ?

There seems to be no way to do so since the sequence of numerators
does not completely define a generalized (irregular) continued
fraction. PARI/GP computes numerators in a greedy manner and for the
sequence of odd squares, it produces:

? contfrac(Pi-3,vector(5,i,(2*i-3)^2))
%1 = [0, 7, 143, 25, 61]

Here
Pi = 3 + 1^2/(7 + 3^2/(143 + 5^2/(25 + 7^2/(61 + ...
is perfectly valid generalized continued fraction with the sequence of
odd squares as partial numerators, however, it is different from the
one mentioned in wikipedia.

Regards,
Max