module Fraction

open common

let reduce (n,d) =
    let g = gcd(n,d)
    (n/g,d/g)

let mul (n1,d1) (n2,d2) =
    (n1 * n2, d1 * d2)

let reciprocal (n,d) = (d,n)

let add (n1,d1) (n2,d2) =
    let f = (n1*d2 + n2*d1, d2*d1)
    reduce f

let reduceI (n:bigint,d:bigint) =
    let g = gcdI(n,d)
    (n/g,d/g)

let mulI (n1:bigint,d1:bigint) (n2:bigint,d2:bigint) =
    reduceI (n1 * n2, d1 * d2)

let reciprocalI (n:bigint,d:bigint) = (d,n)

let addI (n1:bigint,d1:bigint) (n2,d2) =
    let f = (n1*d2 + n2*d1, d2*d1)
    f
    //reduceI f