Bernoulli numbers: Difference between revisions

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 The implementation of the algorithm is in the function bernoullis. The rest is for printing the results.
-<lang Haskell>module Main where
+<lang Haskell>import Data.Ratio
-import Data.Ratio
 import System.Environment
-main = getArgs >>=  printM . defaultArg where
+main = getArgs >>= printM . defaultArg
+  where
-    defaultArg as = if null as then 60 else read (head as)
+    defaultArg as =
+      if null as
+        then 60
+        else read (head as)
+printM m =
-printM m = mapM_ (putStrLn . printP) . takeWhile ((<= m).fst)
+  mapM_ (putStrLn . printP) .
-           . filter (\(_,b) -> b /= 0%1) . zip [0..]  $ bernoullis
+  takeWhile ((<= m) . fst) . filter (\(_, b) -> b /= 0 % 1) . zip [0 ..] $
+  bernoullis
+printP (i, r) =
-printP (i,r) = "B(" ++ show i ++ ")=" ++ show (numerator r) ++ "/" ++ show (denominator r)
+  "B(" ++ show i ++ ") = " ++ show (numerator r) ++ "/" ++ show (denominator r)
-bernoullis =  map head . iterate (ulli 1) . map berno $ enumFrom 0 where
+bernoullis = map head . iterate (ulli 1) . map berno $ enumFrom 0
+  where
-    berno i = 1 % (i+1)
+    berno i = 1 % (i + 1)
     ulli _ [_] = []
-    ulli i (x:y:xs) = (i%1)*(x-y) : ulli (i+1) (y:xs)
+    ulli i (x:y:xs) = (i % 1) * (x - y) : ulli (i + 1) (y : xs)</lang>
+{{Out}}
-</lang>
+<pre>B(0) = 1/1
-{{out}}
+B(1) = 1/2
-<pre>
-B(0)=1/1
+B(2) = 1/6
-B(1)=1/2
+B(4) = -1/30
-B(2)=1/6
+B(6) = 1/42
-B(4)=-1/30
+B(8) = -1/30
-B(6)=1/42
+B(10) = 5/66
-B(8)=-1/30
+B(12) = -691/2730
-B(10)=5/66
+B(14) = 7/6
-B(12)=-691/2730
+B(16) = -3617/510
-B(14)=7/6
+B(18) = 43867/798
-B(16)=-3617/510
+B(20) = -174611/330
-B(18)=43867/798
+B(22) = 854513/138
-B(20)=-174611/330
+B(24) = -236364091/2730
-B(22)=854513/138
+B(26) = 8553103/6
-B(24)=-236364091/2730
+B(28) = -23749461029/870
+B(30) = 8615841276005/14322
-B(26)=8553103/6
-B(28)=-23749461029/870
+B(32) = -7709321041217/510
+B(34) = 2577687858367/6
-B(30)=8615841276005/14322
+B(36) = -26315271553053477373/1919190
-B(32)=-7709321041217/510
-B(34)=2577687858367/6
+B(38) = 2929993913841559/6
+B(40) = -261082718496449122051/13530
-B(36)=-26315271553053477373/1919190
+B(42) = 1520097643918070802691/1806
-B(38)=2929993913841559/6
+B(44) = -27833269579301024235023/690
-B(40)=-261082718496449122051/13530
+B(46) = 596451111593912163277961/282
-B(42)=1520097643918070802691/1806
+B(48) = -5609403368997817686249127547/46410
-B(44)=-27833269579301024235023/690
+B(50) = 495057205241079648212477525/66
-B(46)=596451111593912163277961/282
+B(52) = -801165718135489957347924991853/1590
-B(48)=-5609403368997817686249127547/46410
+B(54) = 29149963634884862421418123812691/798
-B(50)=495057205241079648212477525/66
+B(56) = -2479392929313226753685415739663229/870
-B(52)=-801165718135489957347924991853/1590
+B(58) = 84483613348880041862046775994036021/354
-B(54)=29149963634884862421418123812691/798
+B(60) = -1215233140483755572040304994079820246041491/56786730</pre>
-B(56)=-2479392929313226753685415739663229/870
-B(58)=84483613348880041862046775994036021/354
-B(60)=-1215233140483755572040304994079820246041491/56786730
-</pre>
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