Re: Complex AGM

[John Cremona <john.cremona@gmail.com>]

On 15 February 2012 15:54, Andreas Enge <andreas.enge@inria.fr> wrote:
> On Wed, Feb 15, 2012 at 03:24:21PM +0000, John Cremona wrote:
>> For a definition of what "optimal" means and why it matters for
>> elliptic curve period computations, see http://arxiv.org/abs/1011.0914
>
> In his PhD thesis, Dupont makes the additional assumption that if there
> are two "good" choices, then Im (b_n, a_n) > 0 (it could be that this is
> taken from Cox1984, I have not verified). So I would suggest to modify
> pari to compute the optimal sequence together with this normalisation.

Yes, that is essentially Cox's definition.  But this ambiguous case
only happens at the first step of the algorithm anyway, and when it
does happen the two limits you get by making both choices have exactly
the same absolute value.

John


>
> Andreas