class Density
  include Enumerable
  extend Forwardable

  attr_accessor :uniform, :fail
  def_delegators :@d, :each, :[], :[]=, :inspect, :delete

  def initialize(num=0)
    @d=Hash.new(Rational(0))
    @d[num]=Rational(1)
    @uniform=true
    @fail=false
  end

  # addition of INDEPENDENT densities
  def +(y)
    z=Density.new
    z.delete(0)
    z.uniform=@d.uniform
    z.fail=@d.fail

    if (y.is_a?Density)
      if (y.fail)
        z.fail=true
      end
      if (y.to_a.size>1 and x.to_a.size>1)
        z.uniform=false
      end
      @d.each do |xkey,xvalue|
        y.each do |ykey,yvalue|
          z[xkey+ykey]+=xvalue*yvalue
        end
      end
    elsif (y.is_a?Numeric)
      @d.each do |xkey,xvalue|
        z[xkey+y]+=xvalue
      end
    else
      #TODO
    end
    return z
  end