Bill Allombert on Fri, 13 Jul 2012 21:21:36 +0200

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Re: Possible improvements for bnfcertify and documentation

On Thu, Jul 12, 2012 at 01:19:26PM -0700, John Jones wrote:
> Hi,
> The documentation for bnfinit says that the computation of both the class
> group and fundamental units assumes GRH.  In bnfcertify there is a flag to
> only certify that the class group is a quotient of the one which is
> computed.  It would be good if the documentation would clarify whether or
> not this affects certification of the units.

It certainly affect the certification of the regulator.

> Also, there are fields where pari spends much longer than magma in
> certifying class group/unit data. I don't know the internal algorithms in
> detail, but have the impression that they are doing very similar things,
> but with different bounds.  If so and you can find out what bounds magma
> uses, then maybe pari could use the minimum of its current bound and
> whatever magma is using?

I think it would help if you could provide some example of such field.