rationals.scala

class Rational(initialNumer: Int = 1, initialDenom: Int = 1) {
  require(initialDenom != 0, "denominator must be nonzero")
  
  private val gcd = {
    def gcdRec(x: Int, y: Int): Int = {
      if(y == 0) x else gcdRec(y, x % y)
    }
    abs(gcdRec(initialNumer, initialDenom))
  }
  
  val numer = (if(initialDenom < 0) -abs(initialNumer) else abs(initialNumer)) / gcd
  val denom = abs(initialDenom) / gcd
  
  def unary_- = new Rational(-numer, denom)
    
  def +(that: Rational) =
    new Rational(that.numer * denom + numer * that.denom,
    denom * that.denom)
    
  def -(that: Rational) = this + -that
  def -(that: Int): Rational = this - new Rational(that)
  
  def *(that: Rational) = new Rational(numer * that.numer, denom * that.denom)
  def *(that: Int): Rational = this * new Rational(that)
  
  def /(that: Rational) = new Rational(numer * that.denom, denom * that.numer)
  def /(that: Rational): Rational = this / new Rational(that)
  
  def ==(that: Rational) = that.numer == numer && that.denom == denom
  def ==(that: Int): Rational = this == new Rational(that)
  
  def <(that: Rational) = numer * that.denom < that.numer * denom
  def <(that: Int): Rational = this < new Rational(that)
  
  def >(that: Rational) = !(this < that)
  def >(that: Rational): Rational = this > new Rational(that)
  
  def max(that: Rational) = if (this < that) that else this
  def max(that: Int): Rational = this.max(new Rational(that))
    
  override def toString = numer + "/" + denom
}

object TestRationals extends App {


  
  val r1 = new Rational(3, 5)                     //> r1  : worksheets.Rational = 3/5
  val r2 = new Rational(2, 7)                     //> r2  : worksheets.Rational = 2/7
  val r3 = new Rational(5, 9)                     //> r3  : worksheets.Rational = 5/9
  
  r1 - r2                                         //> res0: worksheets.Rational = 31/35
  
  r1 * r2                                         //> res1: worksheets.Rational = 6/35
  
  r1 == r2                                        //> res2: Boolean = false
  
  r1 / r2                                         //> res3: worksheets.Rational = 21/10
  
  val x = new Rational(1, 3)                      //> x  : worksheets.Rational = 1/3
  val y = new Rational(5, 7)                      //> y  : worksheets.Rational = 5/7
  val z = new Rational(3, 2)                      //> z  : worksheets.Rational = 3/2
  
  x - y - z                                       //> res4: worksheets.Rational = 107/42
  
  val a = new Rational(5)                         //> a  : worksheets.Rational = 5/1
  
  val b = new Rational                            //> b  : worksheets.Rational = 1/1


}