Function: _header_quadratic
Class: header
Section: quadratic
Doc:
 \section{Quadratic number fields and binary quadratic forms}
 This section contains functions related to the arithmetic of quadratic
 number fields. More general functions, more systematic and easier to use,
 apply to general number fields and will be covered in the next sections. To
 study the arithmetic of quadratic fields, you may use either sets of functions
 For instance if you want integral binary quadratic forms (and
 classes) rather than ideals (and ideal classes). The quadratic setting also
 treats non-maximal orders transparently, whereas there is no support for
 non-maximal orders in the general setting.

 We create quadratic numbers using \kbd{quadgen} and binary quadratic
 forms using \kbd{Qfb}. Quadratic numbers are added, multiplied, etc.~using
 standard GP operators (\kbd{+}, \kbd{*}, etc.) and quadratic forms are
 \emph{composed} using \kbd{*}.
 Reduction of forms modulo $\text{SL}(2,\Z)$ is done via \kbd{qfbred} or
 \kbd{qfbredsl2} when the unimodular transformation matrix is desired.
 The functions \kbd{qfbcomp} and \kbd{qfbpow} compute products and powers
 in the class group, incorporating reduction at each step. The function
 \kbd{qfbsolve} solves the equation $q(x,y) = n$ in integers $x,y$.

 The functions \kbd{qfbclassno}, \kbd{quadunit}, \kbd{quadregulator}
 respectively return the \emph{ordinary} (not narrow) class number,
 thefundamental unit, and the regulator. The function \kbd{quadclassunit} is
 asymptotically faster as the discriminant tends to infinity and return the
 (ordinary) class group structure and the regulator of a quadratic order all
 at once, but it is conditional on the GRH. The functions \kbd{quadhilbert}
 and \kbd{quadray} compute Hilbert class fields and ray class fields using
 complex multiplication or Stark units.
