generic
   Dimension : Natural := 3;
package Geometric_Algebra_Generic is

package Real_Arrays is new Ada.Numerics.Generic_Real_Arrays (Float);

type Signature_Type is array (1 .. Dimension) of Integer with
        Default_Component_Value => 1;

subtype Vector_Type is Real_Arrays.Real_Vector (1 .. Get_Dimension);

type Canonic_Base_Element_Type is private;

type Multi_Vector_Type is private;

subtype String_Matrix_Type is HTML.String_Matrix_Type;

type Bit_Type is range 0 .. 1 with
        Default_Value => 0;

type Bit_Array_Type is array (1 .. Dimension) of Bit_Type with
        Default_Component_Value => 0;

type Canonic_Base_Element_Type is record
      Value      : Float            := 0.0;
      Base       : Bit_Array_Type;
      Name       : Unbounded_String := Null_Unbounded_String;
      HTML_Name  : Unbounded_String := Null_Unbounded_String;
      Short_Name : Unbounded_String := Null_Unbounded_String;
      Latex_Name : Unbounded_String := Null_Unbounded_String;
      Grade      : Natural          := 0;
   end record;

type Multi_Vector_Type is array (0 .. Base_Dimension - 1) of Canonic_Base_Element_Type;

Dimension : Natural := 3;

Base_Dimension : constant Natural := 2**Dimension;

Canonic_Base : constant Multi_Vector_Type;

Zero_Multivector : constant Multi_Vector_Type;

One : constant Multi_Vector_Type;

Multi_Vector_not_Inizialised : exception;

Canonic_Base     : constant Multi_Vector_Type := Create_Canonic_Base;

One              : constant Multi_Vector_Type := Create_Canonic_Base;

Zero_Multivector : constant Multi_Vector_Type := Create_Zero_Multivector;

Max_Blade_Length : constant Natural           := Get_Max_Blade_Length;

function Get_Dimension return Natural;

function Scalar_Product 
(
Left, Right
: Vector_Type) return Float;

function "*" 
(
Left
: Canonic_Base_Element_Type;
Right
: Canonic_Base_Element_Type) return Canonic_Base_Element_Type;

procedure Put_Line 
(
Value
: Multi_Vector_Type);

procedure Put_Multi_Vector 
(
Value
: Multi_Vector_Type);

function "+" 
(
Left
: Multi_Vector_Type;
Right
: Multi_Vector_Type) return Multi_Vector_Type;

function "-" 
(
Left
: Multi_Vector_Type;
Right
: Multi_Vector_Type) return Multi_Vector_Type;

function "*" 
(
Left
: Float;
Right
: Multi_Vector_Type) return Multi_Vector_Type;

function "*" 
(
Left
: Multi_Vector_Type;
Right
: Float) return Multi_Vector_Type;

function "*" 
(
Left
: Multi_Vector_Type;
Right
: Multi_Vector_Type) return Multi_Vector_Type;

function "/" 
(
Left
: Multi_Vector_Type;
Right
: Multi_Vector_Type) return Multi_Vector_Type;

procedure Set_Element 
(
Multi_Vector
: in out Multi_Vector_Type;
Element
: Natural;
Value
: Float);

function Get_Base_of_Same_Grad 
(
Grade
: Natural) return Unbounded_String;

function Prepare_Base_Name_Table_ASCII return String_Matrix_Type;

function Prepare_Base_Name_Table_HTML return String_Matrix_Type;

function Prepare_Base_Name_Table_LaTex return String_Matrix_Type;

procedure Create_Base_Vector_Table_HTML 
(
File_Name
: String := "base_vectors_table.html");

procedure Create_Multipikation_Table_HTML 
(
File_Name
: String := "multiplication_table.html");

procedure Create_Multipikation_Table_HTML_Short_Form 
(
File_Name
: String := "multiplication_table_short.html");

procedure Create_Base_Vector_Table_LaTex 
(
File_Name
: String := "base_vectors_table.lat";
Formular_Elements
: Boolean := true);

procedure Create_Multiplication_Table_Latex 
(
File_Name
: String := "multiplication_table.lat");

procedure Create_Multiplication_Table_Latex_Short_Form 
(
File_Name
: String := "multiplication_table.lat");

function Signum 
(
Left
: Bit_Array_Type;
Right
: Bit_Array_Type) return Integer;

function Create_Canonic_Base return Multi_Vector_Type;

function Create_Zero_Multivector return Multi_Vector_Type;

function Get_Max_Blade_Length return Natural;