Re: Component [5] of prime ideal structure

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

On Tue, Feb 11, 2014 at 11:33:48AM +0100, Jeroen Demeyer wrote:
> Consider
> 
> gp> idealprimedec(nfinit(x^2+1), 5)[1][5]
> %4 =
> [2 -1]
> 
> [1  2]
> 
> What is the meaning of this? The documentation ??idealprimedec says
> that it is supposed to be an algebraic integer, but I don't
> understand

Try idealprimedec(nfinit(x^2+1), 5)[1][5][,1]

> it. This changed from PARI-2.5 to PARI-2.6 and it breaks Denis
> Simon's GP scripts.

For reference, this is how Denis ell.gp script is using it:
 valap = idealval(nf,a,p);
  zlog = ideallog(nf,a*(nfbasistoalg(nf,p[5])/p.p)^valap,zinit)
...
  f = idealval(nf,a,p);
  a = nfalgtobasis(nf,a);
  aaa = nfeltpow(nf,nfeltdiv(nf,a,p[5]/p.p),f);
...
  cont = idealval(nf,polcoeff(pol,0),p);
  for( i = 1, deg,
    if( cont, cont = min(cont,idealval(nf,polcoeff(pol,i),p))));
  if( cont, pi = nfbasistoalg(nf,p[5]/p.p));
  if( cont > 1, pol *= pi^(2*(cont\2)));
...

Cheers,
Bill.