Can't you regard the coefficients as a LFSR and then use the
connection polynomial? I'm not saying that there is no work
to be done, but I think the hardest part, the Berlekamp-Massey algorithm,
is implemented.

http://www.sagemath.org/doc/reference/sage/crypto/lfsr.html


On Thu, Jun 24, 2010 at 8:21 PM, John Cremona <john.crem...@gmail.com> wrote:
> I have a power series f(x) in F[[x]] (where F is a finite field) which
> I know to be a rational function p(x)/q(x) where p,q in F[x] have
> degree at most n, and I want to find p and q.  There is an algorithm
> for this, like "rational reconstruction" to go from a real to a
> rational using continued fraction.
>
> I could not find this implemented though there are quite a lot of
> power series utilities and I might not recognise this if it has an
> unfamiliar name.
>
> Does any one know if it is implemented?
>
> John Cremona
>
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