brianberns

open System.Numerics

// http://fsharpnews.blogspot.com/2013/08/implementing-rationals-in-f.html
type Rational(p: BigInteger, q: BigInteger) =
  let rec gcd a (b: BigInteger) =
    if b.IsZero then a else
      gcd b (a % b)

  let fixSign(p: BigInteger, q: BigInteger) =
    if q.Sign > 0 then p, q else -p, -q

brianberns

/// For a function, f, define fix(f) as the "fixed point" of f:
/// A value, z, such that f(z) = z.
///
/// Substituting fix(f) for z, gives f(fix(f)) = fix(f), which
/// we flip to fix(f) = f(fix(f)).
///
/// This fixed point, z, is itself is a function that takes an
/// argument, x. We have to make x explicit in the definition
/// in order to avoid infinite recursion when fix is called.
///