Re: bnfinit new record: degree 105

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Wed, Mar 25, 2015 at 05:51:28AM -0700, William Stein wrote:
> On Wed, Mar 25, 2015 at 5:05 AM, Bill Allombert
> <Bill.Allombert@math.u-bordeaux.fr> wrote:
> > Dear PARI developers,
> >
> > I managed to compute the bnfinit of a degree-105 polynomial, namely
> > polsubcyclo(211,105) which define the field  Q(zeta_211)^+
> >
> > which is named cm/211 in my collezione.
> >
> > The discriminant of the number field is
> > 5.3134347406063639084710374286346095014E241
> >
> > This is both the highest degree and largest discriminant bnfinit succeeded on.
> >
> > The class number is 1 and the regulator is 3.706163881210687671991647261 e88
> >
> > The successful run took 1 hours and 14 minutes.
> >
> > I did not need to tweak bnfinit. It seems bnfinit is well-suited to the
> > fields Q(zeta_p)^+.
> 
> May I ask:
> 
>  (1) exactly what input did you give pari (and with what version)?

bnfinit(polsubcyclo(211,105)) should do.
I used the GIT version (rev 9627612).

>  (2) what's the next similar challenge?

It is not so much a challenge than a way to explore what are the limit of
the implementation.

One conclusion is that, if the size of the discriminant is fixed, then 
bnfinit is faster on fields of large degree than on fields of small degree.

Cheers,
Bill.