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