Re: bnrstark() bug

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

On Thu, 22 Aug 2002, Igor Schein wrote:
> ? bnrstark(bnrinit(bnfinit(y^4-y^3-15*y^2-18*y-4),149,1),Mat(17),1);
>   ***   impossible assignment I-->S

Not really a bug, although the message is misleading.

(15:12) gp > bnrstark(bnrinit(bnfinit(y^4-y^3-15*y^2-18*y-4),149,1),Mat(17),1);
  ***   conductor too large in ComputeArtinNumber.

is better. What triggers the message is that (O_K/f)^* has a very large
cyclic factor [ "large" means >= 2^31 . Here, 149 is inert and 149^4 - 1 is
large...]. Note that the actual limiting factor is Norm(f): the Gauss sum is
computed "naively" and has far too many terms when this is large [ so if you
choose a suitable highly composite conductor, you will have an apparent
infinite loop without triggering the message, since cyclic factors will be
small ].

    Karim.
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Karim Belabas                    Tel: (+33) (0)1 69 15 57 48
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