Karim Belabas on Thu, 22 Jan 2004 19:33:12 +0100

[Date Prev] [Date Next] [Thread Prev] [Thread Next] [Date Index] [Thread Index]

Re: rnfkummer() output issue

* Igor Schein <igor@txc.com> [2004-01-21 05:25]:
> ? p1=rnfkummer(bnrinit(bnfinit(y^8-76*y^6+1425*y^4-5776*y^2+5776),5,1),matdiagonal([2,1]))
> ? nfdisc(p1)
>   ***   polynomial not in Z[X] in nfbasis.
> It's confusing that even though rnfkummer() appears to return an
> absolute polynomial, it in fact isn't, at least internally.  

True. Fixed in CVS.

Btw, I investigated why this example was so slow (5s), and I have slightly
modified rnfnormgroup() so that the computation of p1 is about 4 times faster:
use only places of degree 1 from the base field.

Indeed, they have the same density as arbitrary places in the Galois group of
the ray class field over the base, so we should not lose much.  And computing
in their (prime) residue fields is much easier than in the general case [ we
need to factor the defining relative polynomial in the residue fields ]

Does it break any rnfkummer() thing ?


Karim Belabas                     Tel: (+33) (0)1 69 15 57 48
Dep. de Mathematiques, Bat. 425   Fax: (+33) (0)1 69 15 60 19
Universite Paris-Sud              http://www.math.u-psud.fr/~belabas/ 
F-91405 Orsay (France)            http://pari.math.u-bordeaux.fr/  [PARI/GP]