Function: rnfconductor
Section: number_fields
C-Name: rnfconductor
Prototype: GG
Help: rnfconductor(bnf,T): conductor of the Abelian extension
 of bnf defined by T. The result is [conductor,bnr,subgroup],
 where conductor is the conductor itself, bnr the attached bnr
 structure, and subgroup the HNF defining the norm
 group (Artin or Takagi group) on the given generators bnr.gen.
Doc: given a \var{bnf} structure attached to a number field $K$, as produced
 by \kbd{bnfinit}, and $T$ a monic irreducible polynomial in $K[x]$
 defining an \idx{Abelian extension} $L = K[x]/(T)$, computes the class field
 theory conductor of this Abelian extension. The result is a 3-component vector
 $[\var{conductor},\var{bnr},\var{subgroup}]$, where \var{conductor} is
 the conductor of the extension given as a 2-component row vector
 $[f_0,f_\infty]$, \var{bnr} is the attached \kbd{bnr} structure
 and \var{subgroup} is a matrix in HNF defining the subgroup of the ray class
 group on the ray class group generators \kbd{bnr.gen}.

 \misctitle{Huge discriminants, helping rnfdisc} the format $[T,B]$ is
 also accepted instead of $T$ and computes the conductor of the extension
 provided it factors completely over prime divisors of rational primes $p < B$,
 see \kbd{??rnfinit}: the valuation of $f_0$ is then correct at all prime
 ideals $\goth{p}$ above a rational prime $p < B$ but may be incorrect at other
 primes.
