with Ada.Text_IO; use Ada.Text_IO;
with Ada.Integer_Text_IO; use Ada.Integer_Text_IO;
with Ada.Float_Text_IO; use Ada.Float_Text_IO;

generic

    type T_Element is digits <>;
    N: Positive;

package Google_Naive is

    type T_Google is private;
    type T_Vecteur is private;

    function "*"(left: T_Vecteur ; right: T_Google) return T_Vecteur;
    function "*"(left: Float; right: T_Google) return T_Google;
    function "/"(left: T_Google; right: Float) return T_Google with Pre => right /= 0.0;
    function "+"(left, right: T_Google) return T_Google;

    procedure initialize(mat: in out T_Google);
    procedure initialize(vec: in out T_Vecteur);

    function ones return T_Google;

    procedure insert(mat: in out T_Google; i, j: Natural; elm: T_Element);

    procedure create_H(mat: in out T_Google ; file: in Ada.Text_IO.File_Type);
    procedure create_S(mat: in out T_Google);
    procedure create_G(mat: in out T_Google ; alpha: in Float);

    procedure put(vec: in T_Vecteur);
    procedure put(mat: in T_Google);

    procedure put(file: in out Ada.Text_IO.File_Type; vec: in T_Vecteur);

    procedure sort_with_index_desc(pi: in T_Vecteur; pi_sorted: out T_Vecteur; pi_index: out T_Vecteur);
private

    type T_Google is array (0..N-1, 0..N-1) of T_Element;
    type T_Vecteur is array (0..N-1) of T_Element;

end Google_Naive;