Function: bnrconductor
Section: number_fields
C-Name: bnrconductor0
Prototype: GDGDGD0,L,
Help: bnrconductor(A,{B},{C},{flag=0}): conductor f of the subfield of
 the ray class field given by A,B,C. flag is optional and
 can be 0: default, 1: returns [f, Cl_f, H], H subgroup of the ray class
 group modulo f defining the extension, 2: returns [f, bnr(f), H].
Doc: conductor $f$ of the subfield of a ray class field as defined by $[A,B,C]$
 (of type \kbd{[\var{bnr}]},
 \kbd{[\var{bnr}, \var{subgroup}]},
 \kbd{[\var{bnf}, \var{modulus}]} or
 \kbd{[\var{bnf}, \var{modulus}, \var{subgroup}]},
 \secref{se:CFT})

 If $\fl = 0$, returns $f$.

 If $\fl = 1$, returns $[f, Cl_f, H]$, where $Cl_f$ is the ray class group
 modulo $f$, as a finite abelian group; finally $H$ is the subgroup of $Cl_f$
 defining the extension.

 If $\fl = 2$, returns $[f, \var{bnr}(f), H]$, as above except $Cl_f$ is
 replaced by a \kbd{bnr} structure, as output by $\tet{bnrinit}(,f)$, without
 generators unless the input contained a \var{bnr} with generators.

 In place of a subgroup $H$, this function also accepts a character
 \kbd{chi}  $=(a_j)$, expressed as usual in terms of the generators
 \kbd{bnr.gen}: $\chi(g_j) = \exp(2i\pi a_j / d_j)$, where $g_j$ has
 order $d_j = \kbd{bnr.cyc[j]}$. In which case, the function returns
 respectively

 If $\fl = 0$, the conductor $f$ of $\text{Ker} \chi$.

 If $\fl = 1$, $[f, Cl_f, \chi_f]$, where $\chi_f$ is $\chi$ expressed
 on the minimal ray class group, whose modulus is the conductor.

 If $\fl = 2$, $[f, \var{bnr}(f), \chi_f]$.

Variant:
 Also available is \fun{GEN}{bnrconductor}{GEN bnr, GEN H, long flag}
