Frank Kuehnel schrieb: > 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
Since conj does not need type 'k' I would separate it from class DAlgebra. > 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) This is the way, we defined Complex in NumericPrelude. We have no RealFloat constraint there in order to allow Gaussian numbers and other types. _______________________________________________ Haskell-Cafe mailing list [email protected] http://www.haskell.org/mailman/listinfo/haskell-cafe
