This does not work as expected on Complex numbers due to some odd typechecking hassles apparently associated with abs. How do I get this to typecheck for both real (e.g. Double) and Complex arguments? \begin{code} module Jacobi (sn, cn, dn, sd, cd, nd, cs, ds, ns, sc, dc, nc) where scd x k | abs k < 1e-14 = (sin x, cos x, 1) | otherwise = ((1+m)*s/(1+m*s^2), c*d/(1+m*s^2), (1 - m*s^2)/(1+m*s^2)) where k' = cos $ asin k m = -tanh(log(k')/2) (s, c, d) = scd (x/(1+m)) m sn x k = let (s,_,_) = scd x k in s cn x k = let (_,c,_) = scd x k in c dn x k = let (_,_,d) = scd x k in d sd x k = (sn x k)/(dn x k) cd x k = (cn x k)/(dn x k) nd x k = 1/(dn x k) cs x k = (cn x k)/(sn x k) ds x k = (dn x k)/(sn x k) ns x k = 1/(sn x k) sc x k = (sn x k)/(cn x k) dc x k = (dn x k)/(cn x k) nc x k = 1/(cn x k) \end{code}