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))

(* main *)
let main =
    printfn "%f"  (1./2. + 2./3. * 3./4.)
    let k = (1, 2) ++ (2, 3) ** (3, 4)
    let (a,b) = k
    printfn "%A %f" k (float a / float b)

    let q1 = (-2, 3);
    let q2 = (5, -10);
    let q3 = q1 ++ q2;
    printfn "Test1: %A %A" q3 (naString q3)

    let q35 = q1 -- q2
    printfn "Test2: %A %A" q35 (naString q35)

    let q4 = q2 ** q3
    printfn "Test3: %A %A" q4 (naString q4)

    let q5 = q4 /./ q3
    printfn "Test4: %A %A" q5 (naString q5)

    let q6 = q1 == q2
    printfn "Test5: %A"  q6

    printfn "Test6: %A" (naString q4)
    printfn "Test7: %A" (naString q5)
    0