Bill Allombert on Sat, 05 Mar 2011 20:16:20 +0100

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Re: Question on ellheight algorithm

On Tue, Feb 08, 2011 at 01:16:06PM +1100, Kevin Acres wrote:
> I've spent a while recently with a Tate like method of generating
> values as given by ellheight.  My current gmp implementation takes
> about 5 days to produce a 1000000 digit result, so it's not that
> quick.
> As such I'm interested in writing some code using the gmp library to
> implement Mestre's AGM method.
> Does anyone know if the algorithm is published online or,
> alternatively, point me in the direction of some good information on
> this.

I would suggest 
J.-B. Bost and J.-F. Mestre. Moyenne arithmético-géometrique et périodes
de courbes de genre 1 et 2. Gaz. Math. Soc. France, 38:36­64, 1988. 
but it is in French and it is not available online.

You can start by looking at the function exphellagm in the file
src/basemath/elliptic.c in the PARI distribution.