Re: bnfisintnorm/bnfisnorm and availability of units

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

* Max Alekseyev [2024-08-07 23:01]:
> Hi Karim,
> 
> Thank you for the explanation. The question was really for my understanding
> of the differences between these two functions.
> Performance of bnfisintnorm() in some cases is unsatisfactory as it
> requires too much memory (I raised this issue in another topic earlier this
> year).
> Are there cases when bnfisnorm() has better chances to succeed?

These two functions do fundamentally different things:

- bnfisintnorm returns algebraic *integers* with given norm (in fact,
  all of them, modulo units of norm 1)

- bnfisnorm returns an algebraic *number* (thus allowing denominators!)
  with given norm

Generically, bnfisintnorm (applied to bnfinit(,1)) should be faster and
more robust. But it still returns a completely different output !

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/