X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FTwoTuple.hs;h=becb11eb05435f5a3b45223a5d718475f32e9878;hb=e73e40c515938df4de629dbc88463c5d88bca7c8;hp=8493114ed7cac3dcc956a801127e5b43eca0efef;hpb=06c8df4932b9a46e48b3fc99c3bc44e787b182fc;p=numerical-analysis.git

diff --git a/src/TwoTuple.hs b/src/TwoTuple.hs
index 8493114..becb11e 100644
--- a/src/TwoTuple.hs
+++ b/src/TwoTuple.hs
@@ -1,16 +1,37 @@
 -- | Implement ordered pairs all over again for fun (and to make sure
---   that we can manipulate them algebraically).
+--   that we can manipulate them algebraically). Also require (as
+--   opposed to the built-in ordered pairs) that the elements have
+--   matching types.
 --
 module TwoTuple
 where
 
+import Normed
+
+
 data TwoTuple a = TwoTuple a a
-  deriving (Eq, Show)
+  deriving (Eq)
+
+instance (Show a) => Show (TwoTuple a) where
+  show (TwoTuple x y) = "(" ++ (show x) ++ ", " ++ (show y) ++ ")"
 
 instance Functor TwoTuple where
   f `fmap` (TwoTuple x1 y1) = TwoTuple (f x1) (f y1)
 
+instance (RealFloat a) => Normed (TwoTuple a) where
+  -- The standard Euclidean 2-norm. We need RealFloat for the square
+  -- root.
+  norm (TwoTuple x y) = fromRational $ toRational (sqrt(x^2 + y^2))
+
+  -- The infinity norm, i.e. the maximum entry.
+  norm_infty (TwoTuple x y) =
+    fromRational $ max absx absy
+    where
+      absx = abs (toRational x)
+      absy = abs (toRational y)
 
+-- | It's not correct to use Num here, but I really don't want to have
+--   to define my own addition and subtraction.
 instance Num a => Num (TwoTuple a) where
   -- Standard componentwise addition.
   (TwoTuple x1 y1) + (TwoTuple x2 y2) =