[Cado-nfs-discuss] FactorBaseFormat

Pierrick Gaudry pierrick.gaudry at loria.fr
Sat Feb 3 11:21:24 CET 2018


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

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