Remove assumptions on the Normed class.

[numerical-analysis.git] / src / Normed.hs

diff --git a/src/Normed.hs b/src/Normed.hs
index 8554bd97f2eba0bd66a4b458a05cdb334f2e4f87..3752edc04b9fef7fa04f3ec5fd9a074d5789a0bb 100644 (file)
--- a/src/Normed.hs
+++ b/src/Normed.hs
@@ -1,5 +1,6 @@
 {-# LANGUAGE FlexibleInstances #-}
 {-# LANGUAGE RebindableSyntax #-}
+
 -- | The 'Normed' class represents elements of a normed vector
 --   space. We define instances for all common numeric types.
 module Normed
@@ -8,27 +9,23 @@ where
 import BigFloat
 
 import NumericPrelude hiding (abs)
-import Algebra.Absolute
-import Algebra.Field
-import Algebra.Ring
-import Algebra.ToInteger
+import Algebra.Absolute (abs)
+import qualified Algebra.Absolute as Absolute
+import qualified Algebra.Algebraic as Algebraic
+import qualified Algebra.RealField as RealField
+import qualified Algebra.RealRing as RealRing
+import qualified Algebra.ToInteger as 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 (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
+class Normed a where
+  norm_p :: (ToInteger.C c, Algebraic.C b, Absolute.C b) => c -> a -> b
+  norm_infty :: (RealField.C b) => a -> b
 
   -- | The "usual" norm. Defaults to the Euclidean norm.
-  norm :: (Algebra.Field.C b, Algebra.Absolute.C b) => a -> b
+  norm :: (Algebraic.C b, Absolute.C b) => a -> b
   norm = norm_p (2 :: Integer)
 
 -- Define instances for common numeric types.