Re: Possible improvements for bnfcertify and documentation

On Fri, Jul 13, 2012 at 12:21 PM, Bill Allombert <Bill.Allombert@math.u-bordeaux1.fr> wrote:

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.

Here are two, one with trivial class group and one with a more complicated one.

x^8 - 3*x^7 - 221*x^6 + 1225*x^5 + 11714*x^4 - 98861*x^3 + 68375*x^2 + 909766*x - 1755701

x^8 - 304*x^6 - 1530*x^5 + 20907*x^4 + 212670*x^3 + 610874*x^2 + 298350*x - 695279

John Jones