package Quaternions is

type Quaternion_Real is record
      w, x, y, z : Real;
   end record;

function "abs" 
(
Quad
: Quaternion_Real) return Real;

function Unit  
(
Quad
: Quaternion_Real) return Quaternion_Real;

function Conj  
(
Quad
: Quaternion_Real) return Quaternion_Real;

function "-"   
(
Quad
: Quaternion_Real) return Quaternion_Real;

function "+"   
(
Left, Right
: Quaternion_Real) return Quaternion_Real;

function "-"   
(
Left, Right
: Quaternion_Real) return Quaternion_Real;

function "*"   
(
Left, Right
: Quaternion_Real) return Quaternion_Real;

function "/"   
(
Left, Right
: Quaternion_Real) return Quaternion_Real;

function "*"   
(
Left
: Quaternion_Real;
Right
: Real)            return Quaternion_Real;

function "/"   
(
Left
: Quaternion_Real;
Right
: Real)            return Quaternion_Real;

function "*"   
(
Left
: Real;
Right
: Quaternion_Real) return Quaternion_Real;

function "/"   
(
Left
: Real;
Right
: Quaternion_Real) return Quaternion_Real;

function Image 
(
Quad
: Quaternion_Real) return String;