exception DzieleniePrzezZero

let ( ++ ) (a, b) (c, d) = (a*d + b*c, b*d)
let ( -- ) (a, b) (c, d) = (a*d - b*c, b*d)
let ( ** ) (a, b) (c, d) = (a*c, b*d)
let ( /./ ) (a, b) (c, d) = (a,b) ** (d,c)
let ( == ) (a, b)  (c, d) = (a*d = b*c)

(* najwiekszy wspolny dzielnik *)
let rec NWD = function
    | (0, n) -> n
    | (m, n) -> NWD (n % m, m)


(* skrocenie ulamka *)
let skroc (l, m) =
    let znak = if l * m < 0 then -1 else 1
    let al = abs l
    let am = abs m
    let d = NWD (al, am)
    in (znak * (al / d), am / d)

(* zamiana ulamka na string *)
let naString (l, m) =
   let znak = if l*m<0 then "-" else "" (* deklaracje wewnetrzne *)
   let al = abs l (* wart.bezw. = liczba nat. *)
   let am = abs m
   let d = NWD(al, am)
   in znak + (System.Convert.ToString(al / d))
           + "/" + (System.Convert.ToString(am / d))