1Function: rnfnormgroup 2Section: number_fields 3C-Name: rnfnormgroup 4Prototype: GG 5Help: rnfnormgroup(bnr,pol): norm group (or Artin or Takagi group) 6 corresponding to the Abelian extension of bnr.bnf defined by pol, where 7 the module corresponding to bnr is assumed to be a multiple of the 8 conductor. The result is the HNF defining the norm group on the 9 generators in bnr.gen. 10Doc: 11 \var{bnr} being a big ray 12 class field as output by \kbd{bnrinit} and \var{pol} a relative polynomial 13 defining an \idx{Abelian extension}, computes the norm group (alias Artin 14 or Takagi group) corresponding to the Abelian extension of 15 $\var{bnf}=$\kbd{bnr.bnf} 16 defined by \var{pol}, where the module corresponding to \var{bnr} is assumed 17 to be a multiple of the conductor (i.e.~\var{pol} defines a subextension of 18 bnr). The result is the HNF defining the norm group on the given generators 19 of \kbd{bnr.gen}. Note that neither the fact that \var{pol} defines an 20 Abelian extension nor the fact that the module is a multiple of the conductor 21 is checked. The result is undefined if the assumption is not correct, 22 but the function will return the empty matrix \kbd{[;]} if it detects a 23 problem; it may also not detect the problem and return a wrong result. 24