with Ada.Text_IO; use Ada.Text_IO;
with Ada.Containers.Vectors; use Ada.Containers;
package body GF2n is
    function "+"(X: Element_Type; Y: Element_Type) return Element_Type is
    begin
        return X xor Y;
    end "+";

    function "-"(X: Element_Type; Y: Element_Type) return Element_Type is
    begin
        return X xor Y;
    end "-";

    function "*"(X: Element_Type; Y: Element_Type) return Element_Type is
        Y_In_Bits : Bit_Array;
        Tmp_Element_Type : Element_Type;
        Tmp : Element_Type := 0;
    begin
        Y_In_Bits := Get_Binary(Y);
        for i in Y_In_Bits'Range loop
            if Y_In_Bits(i) = 1 then
                Tmp_Element_Type := Shift_Left(X, i);
                Tmp := Tmp xor Tmp_Element_Type;
            end if;
        end loop;
        return Tmp;
    end "*";

    function "/"(X: Element_Type; Y: Element_Type) return Element_Type is
    begin
        return Shift_Left(X, 1);
    end "/";

    function Find_Inverse(X: Element_Type) return Element_Type is
    begin
        return 1;
    end Find_Inverse;

    function GCD(X: Element_Type; Y: Element_Type) return Element_Type is
    begin
        return 1;
    end GCD;

    function Is_Primitive(X: Element_Type) return Boolean is
    begin
        return True;
    end Is_Primitive;

    function Get_Binary(X: Element_Type) return Bit_Array is
        Bits : Bit_Array := (others => 0);
        Number : Integer := Integer(X);
        Quotient : Integer;
        Bit : Integer;
        Counter : Integer := 0;
    begin
        while Number > 0  loop
            Bit := Number mod 2 ;
            Quotient := Integer(Number / 2);
            Bits(Counter) := Bit;
            Number := Quotient ;
            Counter := Counter + 1;
        end loop;
        return Bits;
    end Get_Binary;
end GF2n;