Re: Pell's equations and beyond

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

* Kurt Foster [2023-12-19 01:28]:
[...]
> If D is composite, and all its prime factors are congruent to 1 (mod 4), I
> don't know how to tell in general whether norm(u) is +1 or -1 other than by
> calculating u.
[...]

In the 'master' branch:

  quadclassunit(D).normfu

If the result is 1, the result is conditional on the GRH. The complexity
is D^ε for any ε > 0 (writing down u is in D^{1/2} in the worst case)

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/