X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FNormed.hs;h=8554bd97f2eba0bd66a4b458a05cdb334f2e4f87;hb=fe73028041fe3becce6ce1ff268181d55d54a011;hp=9bef7631221b9076fe57a261299c98147301233d;hpb=807d976941a8dd426ecf43b18b876413a58384f2;p=numerical-analysis.git

diff --git a/src/Normed.hs b/src/Normed.hs
index 9bef763..8554bd9 100644
--- a/src/Normed.hs
+++ b/src/Normed.hs
@@ -1,41 +1,53 @@
 {-# LANGUAGE FlexibleInstances #-}
-
+{-# LANGUAGE RebindableSyntax #-}
 -- | The 'Normed' class represents elements of a normed vector
 --   space. We define instances for all common numeric types.
 module Normed
 where
 
-import Data.Number.BigFloat
+import BigFloat
+
+import NumericPrelude hiding (abs)
+import Algebra.Absolute
+import Algebra.Field
+import Algebra.Ring
+import Algebra.ToInteger
 
 -- 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
+class (Algebra.Ring.C a, Algebra.Absolute.C a) => Normed a where
+  norm_p :: (Algebra.ToInteger.C c,
+             Algebra.Field.C b,
+             Algebra.Absolute.C b)
+            => c -> a -> b
+
+  norm_infty :: (Algebra.Field.C b,
+                 Algebra.Absolute.C b)
+                => a -> b
 
   -- | The "usual" norm. Defaults to the Euclidean norm.
-  norm :: RealFrac b => a -> b
+  norm :: (Algebra.Field.C b, Algebra.Absolute.C b) => a -> b
   norm = norm_p (2 :: Integer)
 
 -- Define instances for common numeric types.
 instance Normed Integer where
-  norm_p _ = fromInteger
-  norm_infty = fromInteger
+  norm_p _ = abs . fromInteger
+  norm_infty = abs . fromInteger
 
 instance Normed Rational where
-  norm_p _ = realToFrac
-  norm_infty = realToFrac
+  norm_p _ = abs . fromRational'
+  norm_infty = abs . fromRational'
 
 instance Epsilon e => Normed (BigFloat e) where
-  norm_p _ = realToFrac
-  norm_infty = realToFrac
+  norm_p _ = abs . fromRational' . toRational
+  norm_infty = abs . fromRational' . toRational
 
 instance Normed Float where
-  norm_p _ = realToFrac
-  norm_infty = realToFrac
+  norm_p _ = abs . fromRational' . toRational
+  norm_infty = abs . fromRational' . toRational
 
 instance Normed Double where
-  norm_p _ = realToFrac
-  norm_infty = realToFrac
+  norm_p _ = abs . fromRational' . toRational
+  norm_infty = abs . fromRational' . toRational