X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FNormed.hs;h=9bef7631221b9076fe57a261299c98147301233d;hb=c3905924154d9a8d56bdc57e2f36fe48b8524eef;hp=b60c2b12fe84d51e0bf83b60ce0f958af55f7c10;hpb=74e79199dcfec0639133ae9990dc33a2c5a095f0;p=numerical-analysis.git

diff --git a/src/Normed.hs b/src/Normed.hs
index b60c2b1..9bef763 100644
--- a/src/Normed.hs
+++ b/src/Normed.hs
@@ -7,23 +7,35 @@ where
 
 import Data.Number.BigFloat
 
-class Normed a where
+-- Since the norm is defined on a vector space, we should be able to
+-- add and subtract anything on which a norm is defined. Of course
+-- 'Num' is a bad choice here, but we really prefer to use the normal
+-- addition and subtraction operators.
+class (Num a) => Normed a where
   norm_p :: (Integral c, RealFrac b) => c -> a -> b
   norm_infty :: RealFrac b => a -> b
 
+  -- | The "usual" norm. Defaults to the Euclidean norm.
+  norm :: RealFrac b => a -> b
+  norm = norm_p (2 :: Integer)
+
 -- Define instances for common numeric types.
 instance Normed Integer where
   norm_p _ = fromInteger
   norm_infty = fromInteger
 
 instance Normed Rational where
-  norm_p _ = fromRational
-  norm_infty = fromRational
+  norm_p _ = realToFrac
+  norm_infty = realToFrac
 
 instance Epsilon e => Normed (BigFloat e) where
-  norm_p _ = fromRational . toRational
-  norm_infty = fromRational . toRational
+  norm_p _ = realToFrac
+  norm_infty = realToFrac
+
+instance Normed Float where
+  norm_p _ = realToFrac
+  norm_infty = realToFrac
 
 instance Normed Double where
-  norm_p _ = fromRational . toRational
-  norm_infty = fromRational . toRational
+  norm_p _ = realToFrac
+  norm_infty = realToFrac