Data update

Task/Bell-numbers/Haskell/bell-numbers-5.hs

@@ -0,0 +1,17 @@
+import Data.Ratio ((%), numerator)
+
+infixl 7 *.
+(*.) :: Num a => a -> [a] -> [a]
+x *. (p:ps) = x*p : x*.ps
+
+instance Num a => Num [a] where
+    negate = map negate
+    (+) = zipWith (+)
+    (*) (p:ps) (q:qs) = p*q : ((p*.qs) + ps*(q:qs))
+    fromInteger n = fromInteger n:repeat 0
+
+instance (Eq a, Fractional a) => Fractional [a] where
+    (/) (0:ps) (0:qs) = ps/qs
+    (/) (p:ps) (q:qs) = let r=p/q in r : (ps - r*.qs)/(q:qs)
+
+    fromRational q = fromRational q:repeat 0

Task/Bell-numbers/Haskell/bell-numbers-6.hs

@@ -0,0 +1,2 @@
+expseq :: [Rational] -> [Rational]
+expseq ps = zipWith (\p q -> p*fromInteger q) ps (scanl (*) 1 [1..])

Task/Bell-numbers/Haskell/bell-numbers-7.hs

@@ -0,0 +1,3 @@
+infixr 9 |>
+(|>) :: (Eq a, Num a) => [a] -> [a] -> [a]
+(p:ps) |> (0:qs) = p : qs*(ps |> (0:qs))

Task/Bell-numbers/Haskell/bell-numbers-8.hs

@@ -0,0 +1,11 @@
+exp1 :: [Rational]
+exp1 = 0 : map (1%) factorials
+  where
+    factorials = scanl (*) 1 [2..]
+
+exps :: [Rational]
+exps = 1 : zipWith (*) exps [ 1%n | n <- [1..] ]
+
+bell :: [Integer]
+bell = map numerator
+    (expseq (exps |> exp1))

Task/Bell-numbers/Haskell/bell-numbers-9.hs

@@ -0,0 +1,4 @@
+ghci> take 15 bell
+[1,1,2,5,15,52,203,877,4140,21147,115975,678570,4213597,27644437,190899322]
+ghci> bell !! 49
+10726137154573358400342215518590002633917247281