[Cado-nfs-discuss] FactorBaseFormat

Pankaj Charpe charpe.pankajamol at gmail.com
Sat Feb 3 15:42:49 CET 2018


Thanks for the reply. I have studied your thesis. p and r (roots) are clear
to me but I am not getting any explanation for those n1 and n2. Can you
elaborate their use? I would really appreciate your reply. I also mailed
via mailing list.

Thanks & Regards
Pankaj Charpe

On Feb 3, 2018 5:30 PM, "Emmanuel Thomé" <emmanuel.thome at inria.fr> wrote:

> Yes.
> Actually log(p) would be less misleading than degree(p)...
> E.
>
>
> On February 3, 2018 11:21:24 AM GMT+01:00, Pierrick Gaudry <
> pierrick.gaudry at loria.fr> wrote:
> >Hi,
> >
> >From an old README file I have somewhere in an old directory:
> >
> >    Factor base file format:
> >    ------------------------
> >
> >    An entry is of the form:
> >
> >    q:n1,n2: r1,r2,r3
> >
> >    In the (frequent) case where n1,n2=1,0 this can be abridged with:
> >
> >    q: r1,r2,r3
> >
> >Here, q is a irreducible or a irreducible power, ri are the
> >corresponding
> >roots and the contribution that must be subtracted at these positions
> >is
> >    (n1-n2)*degree(p) (assuming smaller powers of this irreducible have
> >  alredy been taken care of).  By position, we mean (a,b) such that a -
> >    b*ri = 0 mod q.
> >
> > The roots ri must be sorted in lexicographical order.  If a root ri is
> >    greater or equal to q, it means that this is a projective root:
> >    subtracting q gives a root for the reciprocal polynomial (or
> >    equivalently, (1:(ri-q)) is the projective root).
> >
> > It is allowed to have several lines with the same q, but there must be
> >    only one line for a given (q,n1,n2) triple.
> >
> >Hopefully this is still valid in the version you are using.
> >
> >Regards,
> >Pierrick
> >
> >On Sat, Feb 03, 2018 at 01:50:46PM +0530, Pankaj Charpe wrote:
> >> Hi,
> >>  In factor base construction of cado-nfs we have this entry,
> >>                             Factor Base format: q:n1,n2:r1,r2,r3
> >>
> >> Can you please explain me what is these n1 and n2 ?. I will be very
> >> thankful to you.
> >>
> >>
> >> Thanks & Regards
> >> Pankaj charpe
> >
> >> _______________________________________________
> >> Cado-nfs-discuss mailing list
> >> Cado-nfs-discuss at lists.gforge.inria.fr
> >> https://lists.gforge.inria.fr/mailman/listinfo/cado-nfs-discuss
> >
> >_______________________________________________
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>
> --
> Sent from my phone. Please excuse brevity and misspellings.
>
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