Re: P-Adic Point Counting Question

From: Anthony Mulcahy (anthony_at_kcn.ne.jp)
Date: 01/19/04 

Date: Tue, 20 Jan 2004 06:10:48 +0900

"Robert Harley" <harley@estephe.inria.fr> wrote in message
news:rz7ektwqt7s.fsf@estephe.inria.fr...
>
> Anthony Mulcahy writes:
> >In the algorithms described in the paper "An extension of Satoh's
> >algorithm and its implementation" [...] there are equations such as
> >"1 - 504Z + 22A" [...] These equations appear to mix integers such as
> >1, 504, 22 and 864 with elements of the p-adic ring [...]
>
> You can map the integers into the ring, just as you would into any
> ring with identity. Map the natural integer 1 to the p-adic integer 1,
> then 2 to 1+1, or in general n to 1+1+...+1 repeated n times.
> If you are comfortable thinking of p-adic integers as little-endian
> sequences of base-p digits (for instance) then think of finding the
> base-p expansion of n and appending zeroes ad infinitum e.g.,
> 16 = 1*3^0+2*3^1+1*3^2 so it would map to the sequence 1,2,1,0,0,0,...
>
> Hope this helps,
> Rob.

Thanks very much for the explanation. This clarifies things.

Best regards,

Anthony Mulcahy

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