module Polynomials
  class Point
    include Comparable
    attr_accessor :x, :y

    def self.inherited(subclass)
      self.class_eval do 
        define_method :"#{subclass.name.demodulize.underscore}?" do
          self.is_a? subclass
        end
      end
    end
    def initialize(x,y)
      @x,@y = x,y
    end

    def to_s
      "(#{self.x.inspect},#{self.y.inspect})"
    end

    def <=>(other)
      if self.x < other.x
        -1
      elsif self.x > other.x
        1
      elsif self.x == other.x && self.y == other.y
        0
      end
    end

    def eql?(other)
      self.x == other.x &&
        self.y == other.y &&
        other.class == self.class
    end
  end

  class Extremum < Point
    attr_accessor :kind_of_extremum

    [:maximum,:minimum].each do |extremum|
      self.superclass.class_eval do
        define_method :"#{extremum}?" do
          self.extremum? && self.kind_of_extremum == extremum
        end
      end
    end

    def initialize(*args,kind_of_extremum)
      @kind_of_extremum = kind_of_extremum
      super(*args)
    end

    def to_s
      super + kind_of_extremum.to_s
    end

    def eql?(other)
      super && self.kind_of_extremum == other.kind_of_extremum
    end
  end

  class Root < Point
    def initialize(x)
      super(x,0)
    end
  end

  class InflectionPoint < Point
  end
end