Re: Pell's equations and beyond

[Denis Simon <denis.simon@unicaen.fr>]

Hi,

If norm(u) = 1, is there a quick way to test whether this u is a square or not ?

Denis.

----- Mail original -----
> De: "Karim Belabas" <Karim.Belabas@math.u-bordeaux.fr>
> À: "Kurt Foster" <drsardonicus@earthlink.net>
> Cc: "Pari Users" <pari-users@pari.math.u-bordeaux.fr>
> Envoyé: Mardi 19 Décembre 2023 10:06:03
> Objet: Re: Pell's equations and beyond

> * 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/