Clean up imports everywhere.

[numerical-analysis.git] / src / Integration / Trapezoid.hs

diff --git a/src/Integration/Trapezoid.hs b/src/Integration/Trapezoid.hs
index c358feffec5d536f913d8e3a1c080391b17762d4..df4da781b6cea30e7fbe763ee20da9ba85549db7 100644 (file)
--- a/src/Integration/Trapezoid.hs
+++ b/src/Integration/Trapezoid.hs
@@ -1,17 +1,19 @@
+{-# LANGUAGE NoImplicitPrelude #-}
 {-# LANGUAGE RebindableSyntax #-}
 
-module Integration.Trapezoid
+module Integration.Trapezoid (
+  trapezoid,
+  trapezoid_1 )
 where
 
-import Misc (partition)
+import Misc ( partition )
+
+import NumericPrelude hiding ( abs )
+import qualified Algebra.Field as Field ( C )
+import qualified Algebra.RealField as RealField ( C )
+import qualified Algebra.ToInteger as ToInteger ( C )
+import qualified Algebra.ToRational as ToRational ( C )
 
-import NumericPrelude hiding (abs)
-import Algebra.Absolute (abs)
-import qualified Algebra.Field as Field
-import qualified Algebra.RealField as RealField
-import qualified Algebra.RealRing as RealRing
-import qualified Algebra.ToInteger as ToInteger
-import qualified Algebra.ToRational as ToRational
 
 -- | Use the trapezoid rule to numerically integrate @f@ over the
 --   interval [@a@, @b@].
@@ -40,19 +42,22 @@ trapezoid_1 :: (Field.C a, ToRational.C a, Field.C b)
             -> a       -- ^ The \"right\" endpoint, @b@
             -> b
 trapezoid_1 f a b =
-  (((f a) + (f b)) / 2) * (fromRational' $ toRational (b - a))
-
+  (((f a) + (f b)) / 2) * coerced_interval_length
+  where
+    coerced_interval_length = fromRational' $ toRational (b - a)
 
 -- | Use the composite trapezoid rule to numerically integrate @f@
 --   over @n@ subintervals of [@a@, @b@].
 --
 --   Examples:
 --
+--   >>> import Algebra.Absolute (abs)
 --   >>> let f x = x^2
 --   >>> let area = trapezoid 1000 f (-1) 1
 --   >>> abs (area - (2/3)) < 0.00001
 --   True
 --
+--   >>> import Algebra.Absolute (abs)
 --   >>> let area = trapezoid 1000 sin 0 pi
 --   >>> abs (area - 2) < 0.0001
 --   True