Re: helping nfinit

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

* John Cremona [2026-05-14 12:04]:
> Also, the situation I am in is that as well as a polynomial pol (monic
> irreducible and integral) defining the field, I have a collection of
> known algebraic integers a2=Mod(g2,pol), a3=Mod(g3,pol), ....   It
> seems that knowing these should help nfinit but I don't see an easy
> way of doing so.

Not trivial in GP. You can use

  install(ZV_cba, mG)

then

- apply ZV_cba(A) to the vector A of poldisc(minpoly(a[i])) and poldisc(pol).
This returns a coprime basis B attached to A. I.e., a
vector of pairwise coprime integers such that all the A[i] is is product
of the B[j].

- factor the individual B[j] dividing poldisc(pol), concatenate the
  resulting primes and feed that to nfbasis

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/