Hi folks, how do I make this work: I want a division algebra over a field k, and I want to define the conjugation of complex numbers, i.e. conj (C 1 2) but also the conjugation of tensors of complex numbers conj (C (C 1 2) (C 1 4)) ghci load that stuff butt barfs on a simple
conj (C 1 2)
with instance Real a => DAlgebra a a -- Defined at Clifford.hs:20:10-31 instance (Real r, Num a, DAlgebra a r) => DAlgebra (Complex a) r here's the code: -- for a normed division algebra we need a norm and conjugation! class DAlgebra a k | a -> k where -- need functional dependence because conj doesn't refer to k conj :: a -> a abs2 :: a -> k -- real numbers are a division algebra instance Real a => DAlgebra a a where conj = id abs2 x = x*x -- Complex numbers form a normed commutative division algebra data Complex a = C a a deriving (Eq,Show) instance Num a => Num (Complex a) where fromInteger a = C (fromInteger a) 0 (C a b)+(C a' b') = C (a+a') (b+b') (C a b)-(C a' b') = C (a-a') (b-b') (C a b)*(C a' b') = C (a*a'-b*b') (a*b'+b*a') instance (Real r, Num a, DAlgebra a r) => DAlgebra (Complex a) r where conj (C a b) = C a (conj (-b)) abs2 (C a b) = (abs2 a) + (abs2 b) Thanks for you help!