module Algebra.NormedSpace.Euclidean where
import PreludeBase
import NumericPrelude (sqr, abs, (+), sum, Float, Double, Int, Integer, )
import qualified Number.Ratio as Ratio
import qualified Algebra.PrincipalIdealDomain as PID
import qualified Algebra.Algebraic as Algebraic
import qualified Algebra.Real as Real
import qualified Algebra.Module as Module
class (Real.C a, Module.C a v) => Sqr a v where
normSqr :: v -> a
class (Sqr a v) => C a v where
norm :: v -> a
defltNorm :: (Algebraic.C a, Sqr a v) => v -> a
defltNorm = Algebraic.sqrt . normSqr
instance Sqr Float Float where
normSqr = sqr
instance C Float Float where
norm = abs
instance Sqr Double Double where
normSqr = sqr
instance C Double Double where
norm = abs
instance Sqr Int Int where
normSqr = sqr
instance C Int Int where
norm = abs
instance Sqr Integer Integer where
normSqr = sqr
instance C Integer Integer where
norm = abs
instance (Real.C a, PID.C a) => Sqr (Ratio.T a) (Ratio.T a) where
normSqr = sqr
instance (Sqr a v0, Sqr a v1) => Sqr a (v0, v1) where
normSqr (x0,x1) = normSqr x0 + normSqr x1
instance (Algebraic.C a, Sqr a v0, Sqr a v1) => C a (v0, v1) where
norm = defltNorm
instance (Sqr a v0, Sqr a v1, Sqr a v2) => Sqr a (v0, v1, v2) where
normSqr (x0,x1,x2) = normSqr x0 + normSqr x1 + normSqr x2
instance (Algebraic.C a, Sqr a v0, Sqr a v1, Sqr a v2) => C a (v0, v1, v2) where
norm = defltNorm
instance (Sqr a v) => Sqr a [v] where
normSqr = sum . map normSqr
instance (Algebraic.C a, Sqr a v) => C a [v] where
norm = defltNorm