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Karim Belabas on Thu, 08 Aug 2024 13:55:30 +0200
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Re: bnfisintnorm/bnfisnorm and availability of units
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- To: Max Alekseyev <maxale@gmail.com>
- Subject: Re: bnfisintnorm/bnfisnorm and availability of units
- From: Karim Belabas <Karim.Belabas@math.u-bordeaux.fr>
- Date: Thu, 8 Aug 2024 13:55:14 +0200
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- Cc: Pari Users <pari-users@pari.math.u-bordeaux.fr>
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* 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/