Re: helping nfinit

[Karim Belabas <Karim.Belabas@u-bordeaux.fr>]

* Bill Allombert [2026-05-14 12:57]:
> On Thu, May 14, 2026 at 11:03:31AM +0100, John Cremona wrote:
> > In gp, ?nfinit says that the first parameter must be a polynomial.
> > The longer documentation in ??nfinit says that the first parameter can
> > be a pair or triple [pol,B], [pol,B,P] or [pol,listP] where B is a
> > lift of an integral basis, P and listP are lists of primes.   But the
> > example given if nfinit([pol,10^3]) which shows that the second
> > parameter can be a bound on the primes and not just a list of primes.
> > Perhaps this should be corrected (if I am right)?
> 
> See ??nfbasis.

More precisely, ??nfinit states that "listP specifies a list of
primes as in nfbasis".

Three different kinds of data can be used to "specify" this list: actual
vector of primes, all primes up to some (small) positive bound,
(partial) factorization matrix for the discriminant. Those are described
in about 10 lines in ??nfbasis and won't be replicated in the 10+
functions that allow such inputs. The reference to nfbasis should be
present in all of them, though.

Cheers,

    K.B.
-- 
Pr. Karim Belabas, U. Bordeaux, Vice-président en charge du Numérique
Institut de Mathématiques de Bordeaux UMR 5251 - (+33) 05 40 00 29 77
http://www.math.u-bordeaux.fr/~kbelabas/