Add all the A tasks

Task/Arithmetic-Rational/Scala/arithmetic-rational-1.scala

@@ -0,0 +1,44 @@
+class Rational(n: Long, d:Long) extends Ordered[Rational]
+{
+   require(d!=0)
+   private val g:Long = gcd(n, d)
+   val numerator:Long = n/g
+   val denominator:Long = d/g
+
+   def this(n:Long)=this(n,1)
+
+   def +(that:Rational):Rational=new Rational(
+      numerator*that.denominator + that.numerator*denominator,
+      denominator*that.denominator)
+
+   def -(that:Rational):Rational=new Rational(
+      numerator*that.denominator - that.numerator*denominator,
+      denominator*that.denominator)
+
+   def *(that:Rational):Rational=
+      new Rational(numerator*that.numerator, denominator*that.denominator)
+
+   def /(that:Rational):Rational=
+      new Rational(numerator*that.denominator, that.numerator*denominator)
+
+   def unary_~ :Rational=new Rational(denominator, numerator)
+
+   def unary_- :Rational=new Rational(-numerator, denominator)
+
+   def abs :Rational=new Rational(Math.abs(numerator), Math.abs(denominator))
+
+   override def compare(that:Rational):Int=
+      (this.numerator*that.denominator-that.numerator*this.denominator).toInt
+
+   override def toString()=numerator+"/"+denominator
+
+   private def gcd(x:Long, y:Long):Long=
+      if(y==0) x else gcd(y, x%y)
+}
+
+object Rational
+{
+   def apply(n: Long, d:Long)=new Rational(n,d)
+   def apply(n:Long)=new Rational(n)
+   implicit def longToRational(i:Long)=new Rational(i)
+}

Task/Arithmetic-Rational/Scala/arithmetic-rational-2.scala

@@ -0,0 +1,15 @@
+def find_perfects():Unit=
+{
+   for (candidate <- 2 until 1<<19)
+   {
+      var sum= ~Rational(candidate)
+      for (factor <- 2 until (Math.sqrt(candidate)+1).toInt)
+      {
+         if (candidate%factor==0)
+            sum+= ~Rational(factor)+ ~Rational(candidate/factor)
+      }
+
+      if (sum.denominator==1 && sum.numerator==1)
+         printf("Perfect number %d sum is %s\n", candidate, sum)
+   }
+}