// code examples from Scala by Example, chapter 6, 
// 


class Rational(n: Int, d: Int) {
  private def gcd(x: Int, y: Int): Int = {
    if (x == 0) y
    else if (x < 0) gcd(-x,y)
    else if (y < 0) -gcd(x, -y)
    else gcd(y % x, x)
  }
  private val g = gcd(n, d)

  val numer: Int = n/g
  val denom: Int = d/g

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

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

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

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


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

  def square = new Rational(numer*numer, denom*denom)
}


def sumOfFractions (max: Int): Rational = {
  var i = 1
  var sum = new Rational(0, 1)
  while (i <= max) {
    sum += new Rational(1, i)
    i += 1
  }
  sum
}


// can you do a (tail) recursive version of sumOfFractions ?


// in Scala, every class extends class "AnyRef"  (cf. Object in Java)

var x: AnyRef = sumOfFractions(2) 

// try:  x * new Rational(3 ,4 )
// try:  x.asInstanceOf[Rational] * new Rational(3 ,4 )


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