Rational

package example

class Rational(x: Int, y: Int) {
  require(y!=0, "denom cannot be zero")

  def this(x:Int) = this (x,1)

  private def gcd(a:Int, b:Int):Int = if (b==0) a else gcd(b, a%b)
  private val g = gcd(x,y)

  val numer = x
  val denom = y

  def < (that:Rational) = numer*that.denom < denom*that.numer
  def max(that: Rational) = if(this < that) that else this

  def +(that: Rational) =
    new Rational((numer * that.denom + that.numer * denom), denom * that.denom)

  override def toString = numer/g + "/" + denom/g

  def unary_- :Rational = new Rational(-numer, denom)

  def - (that: Rational) = this + -that

}

object rationals {
  val k = new Rational(4)
  val x = new Rational(1, 3)
  x.numer
  x.denom
  val y = new Rational(5, 7)
  val z = new Rational(3, 2)
  y < z
  z.toString
  -x
  x - y
  y + y
  x - y - z
}