[Cado-nfs-discuss] FactorBaseFormat

Pierrick Gaudry pierrick.gaudry at loria.fr
Tue Feb 6 14:33:40 CET 2018


Hi,

The full story is computing the maximal order of a number (or function)
field, which is closely related to factoring polynomials over p-adic
numbers (or power series).

This is covered, for instance, in Chapter 6 of Cohen's book "A course in
computational algrebraic number theory". In Cado-nfs 2.3, this is
implemented in the numbertheory/ subdirectory.

However, for makefb, only a very partial information is sufficient, so
that a simpler Hensel-like procedure is used. For this part, as far as I
know there is no article or book describing it. The sage source:
  sieve/makefb.sage
might be easier to understand than the C code. But in the end, the main
keyword is: Hensel. You know what's going on modulo p^k and compute what
it yields modulo p^{k+1} until you reach some regular pattern.

Regards,
Pierrick

On Mon, Feb 05, 2018 at 04:31:01PM +0530, Pankaj Charpe wrote:
> can you please provide a link to any reference paper to study this?  It
> will be very helpful to me.
> 
> -pankaj


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