Re: ideal principal in relative extension

[Bill Allombert <Bill.Allombert@math.u-bordeaux1.fr>]

On Sun, Jan 01, 2012 at 10:10:43AM +0000, zekhnini wrote:
>   
> Dear users,
>  I want to know if the thow ideals M and N are principal in the relative     
> extension K=k(sqrt(2+8*i)) of the field k=Q(sqrt(2*17*5),i ). what can I do?
> 
>  
>   T=polcompositum(y^2+1,y^2-2*17*5)[1];
>   k=nfinit(T);
>   P=x^2-Mod(y^4-4*y^2+4*17,k.pol);
> 
>   K=rnfinit(k,P);
>   Keqn=rnfequation(k,P,1)[1];
>   Kabs=nfinit(Keqn);          
>   
>   H1=idealprimedec(k,17)[1];
>   H2=idealprimedec(k,17)[2];
>   
>   M=rnfidealup(K,H1);
>   N=rnfidealup(K,H2);
> 
> 
>   MK= mathnf( Mat( nfalgtobasis(Kabs, M) ) );
>   NK= mathnf( Mat( nfalgtobasis(Kabs, N) ) );
> 
>  It responds  nfalgtobasis: incorrect type in algtobasis.

You should use matalgtobasis instead of nfalgtobasis.
There is a typo in the documentation of rnfidealup in PARI 2.5.0, the
function idealgentoHNF should be:

idealgentoHNF(nf, y) = mathnf( Mat( matalgtobasis(nf, y) ) );

Cheers,
Bill.