Decomposition of ideals in hard case.

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

Hello PARI dev,

I would like to compute the decomposition of a prime number
in a number field, in hard case.

Hard case mean the prime number divide the index of the defining
polynomial, I don't have the nfinit() around, and probably I cannot
factor the discriminant of the polynomial.

I use the code below:

decomp(P,p)=
{
  d=poldisc(P);
  B=nfbasis(P,,Mat([p,valuation(d,p)]));
  /*B is a basis of a p-maximal order*/
  K=nfinit([G.pol,B],1);
  idealprimedec(K,p)
}

As an example try P=x^54 + 796392*x^36 + 292918032*x^18 + 1259712.
I don't neccessarily need all the info given by idealprimedec.
The ramification and residual degrees can be enough in some case.

Can it be done faster? The call to nfinit() seems to waste time
doing too much things.

Cheers,
Bill.