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.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@
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@
-- We also return the number of iterations required.
--
fixed_point_with_iterations :: (Normed a,
- Algebra.Field.C b,
- Algebra.Absolute.C b,
- Ord b)
+ Additive.C a,
+ RealField.C b,
+ Algebraic.C b)
=> (a -> a) -- ^ The function @f@ to iterate.
-> b -- ^ The tolerance, @epsilon@.
-> a -- ^ The initial value @x0@.