Remove assumptions on the Normed class.

[numerical-analysis.git] / src / Roots / Simple.hs

diff --git a/src/Roots/Simple.hs b/src/Roots/Simple.hs
index 0a1debff0a0b1db653efabdf2be00ce9a4b91ed4..d3c10cd8a3dfb95c001aeb5ce244b1bc7f14f7ed 100644 (file)
--- a/src/Roots/Simple.hs
+++ b/src/Roots/Simple.hs
@@ -20,6 +20,8 @@ import qualified Roots.Fast as F
 import NumericPrelude hiding (abs)
 import qualified Algebra.Absolute as Absolute
 import Algebra.Absolute (abs)
+import qualified Algebra.Additive as Additive
+import qualified Algebra.Algebraic as Algebraic
 import qualified Algebra.Field as Field
 import qualified Algebra.RealField as RealField
 import qualified Algebra.RealRing as RealRing
@@ -87,7 +89,7 @@ bisect f a b epsilon =
 --   at x0. We delegate to the version that returns the number of
 --   iterations and simply discard the number of iterations.
 --
-fixed_point :: (Normed a, RealField.C b)
+fixed_point :: (Normed a, Algebraic.C a, Algebraic.C b, RealField.C b)
             => (a -> a) -- ^ The function @f@ to iterate.
             -> b       -- ^ The tolerance, @epsilon@.
             -> a       -- ^ The initial value @x0@.
@@ -100,7 +102,10 @@ fixed_point f epsilon x0 =
 --   the function @f@ with the search starting at x0 and tolerance
 --   @epsilon@. We delegate to the version that returns the number of
 --   iterations and simply discard the fixed point.
-fixed_point_iteration_count :: (Normed a, RealField.C b)
+fixed_point_iteration_count :: (Normed a,
+                                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@.
@@ -118,7 +123,10 @@ fixed_point_iteration_count f epsilon x0 =
 --
 --   This is used to determine the rate of convergence.
 --
-fixed_point_error_ratios :: (Normed a, RealField.C b)
+fixed_point_error_ratios :: (Normed a,
+                             Additive.C a,
+                             RealField.C b,
+                             Algebraic.C b)
                    => (a -> a) -- ^ The function @f@ to iterate.
                    -> a       -- ^ The initial value @x0@.
                    -> a       -- ^ The true solution, @x_star@.