X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FRoots%2FFast.hs;h=0deb1fd6237a5909ea7d15a252f09b524093d1bf;hb=d52e10c90c0b8263af2e6a0152cebf0ad3c70e62;hp=47fa512a75476310403d1faed03b9c54bdabe171;hpb=fe73028041fe3becce6ce1ff268181d55d54a011;p=numerical-analysis.git

diff --git a/src/Roots/Fast.hs b/src/Roots/Fast.hs
index 47fa512..0deb1fd 100644
--- a/src/Roots/Fast.hs
+++ b/src/Roots/Fast.hs
@@ -13,15 +13,16 @@ import Data.List (find)
 import Normed
 
 import NumericPrelude hiding (abs)
-import Algebra.Absolute
-import Algebra.Field
-import Algebra.Ring
-
-has_root :: (Algebra.Field.C a,
-             Ord a,
-             Algebra.Ring.C b,
-             Ord b,
-             Algebra.Absolute.C b)
+import qualified Algebra.Absolute as Absolute
+import qualified Algebra.Additive as Additive
+import qualified Algebra.Algebraic as Algebraic
+import qualified Algebra.Field as Field
+import qualified Algebra.RealRing as RealRing
+import qualified Algebra.RealField as RealField
+
+has_root :: (RealField.C a,
+             RealRing.C b,
+             Absolute.C b)
          => (a -> b) -- ^ The function @f@
          -> a       -- ^ The \"left\" endpoint, @a@
          -> a       -- ^ The \"right\" endpoint, @b@
@@ -61,11 +62,9 @@ has_root f a b epsilon f_of_a f_of_b =
     c = (a + b)/2
 
 
-bisect :: (Algebra.Field.C a,
-           Ord a,
-           Algebra.Ring.C b,
-           Ord b,
-           Algebra.Absolute.C b)
+bisect :: (RealField.C a,
+           RealRing.C b,
+           Absolute.C b)
        => (a -> b) -- ^ The function @f@ whose root we seek
        -> a       -- ^ The \"left\" endpoint of the interval, @a@
        -> a       -- ^ The \"right\" endpoint of the interval, @b@
@@ -119,9 +118,9 @@ fixed_point_iterations f x0 =
 --   We also return the number of iterations required.
 --
 fixed_point_with_iterations :: (Normed a,
-                                Algebra.Field.C b,
-                                Algebra.Absolute.C b,
-                                Ord b)
+                                Algebraic.C a,
+                                RealField.C b,
+                                Algebraic.C b)
                             => (a -> a)  -- ^ The function @f@ to iterate.
                             -> b        -- ^ The tolerance, @epsilon@.
                             -> a        -- ^ The initial value @x0@.