Task

Create a reasonably complete implementation of rational arithmetic in the particular language using the idioms of the language.



Example

Define a new type called frac with binary operator "//" of two integers that returns a structure made up of the numerator and the denominator (as per a rational number).

Further define the appropriate rational unary operators abs and '-', with the binary operators for addition '+', subtraction '-', multiplication '×', division '/', integer division '÷', modulo division, the comparison operators (e.g. '<', '≤', '>', & '≥') and equality operators (e.g. '=' & '≠').

Define standard coercion operators for casting int to frac etc.

If space allows, define standard increment and decrement operators (e.g. '+:=' & '-:=' etc.).

Finally test the operators:
Use the new type frac to find all perfect numbers less than 219 by summing the reciprocal of the factors.



Related task

   Perfect Numbers


for n in (1 .. 2**19) {
    var frac = 0
 
    n.divisors.each {|d|
        frac += 1/d
    }
 
    if (frac.is_int) {
        say "Sum of reciprocal divisors of #{n} = #{frac} exactly #{
            frac == 2 ? '- perfect!' : ''
        }"
    }
}