+-- | We are given a function @f@ and an interval [a,b]. The trisection
+-- method finds a root by splitting [a,b] into three
+-- subintervals repeatedly.
+--
+-- If one is found within some prescribed tolerance @epsilon@, it is
+-- returned. Otherwise, the interval [a,b] is split into two
+-- subintervals [a,c] and [c,b] of equal length which are then both
+-- checked via the same process.
+--
+-- Returns 'Just' the value x for which f(x) == 0 if one is found,
+-- or Nothing if one of the preconditions is violated.
+--
+-- Examples:
+--
+-- >>> let actual = 1.5707963267948966
+-- >>> let Just root = trisect cos 1 2 0.001
+-- >>> root
+-- 1.5713305898491083
+-- >>> abs (root - actual) < 0.001
+-- True
+--
+-- >>> trisect sin (-1) 1 0.001
+-- Just 0.0
+--
+trisect :: (RealField.C a, RealRing.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@
+ -> a -- ^ The tolerance, @epsilon@
+ -> Maybe a
+trisect f a b epsilon =
+ F.trisect f a b epsilon Nothing Nothing
+
+