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