Data update

Task/Bell-numbers/BQN/bell-numbers.bqn

@@ -0,0 +1,8 @@
+Bell ← {(+`⊢´⊸∾)⍟(↕𝕩)⋈1}
+
+•Out "First 15 Bell numbers:"
+•Show ⊑¨ Bell 15
+
+•Out ""
+•Out "First 10 rows of the Bell triangle:"
+•Show¨ Bell 10

Task/Bell-numbers/Forth/bell-numbers.fth

@@ -0,0 +1,51 @@
+: triangle-allocate ( u -- addr )
+  dup 1+ * 2/ cells dup
+  allocate abort" out of memory"
+  tuck swap erase ;
+
+: triangle-deallocate ( addr -- )
+  free abort" memory deallocation error" ;
+
+: triangle-row-address ( addr u -- addr )
+  dup 1+ * 2/ cells + ;
+
+: bell-triangle-row ( addr u -- )
+  tuck 1- triangle-row-address
+  2dup swap cells +
+  dup 1 cells - @ over !
+  rot 0 ?do
+    dup @ >r over @ r> + >r
+    cell+ r> over !
+    swap cell+ swap
+  loop 2drop ;
+
+: bell-triangle ( u -- addr )
+  dup triangle-allocate
+  dup 1 swap !
+  swap 1 ?do
+    dup i bell-triangle-row
+  loop ;
+
+: print-bell-numbers ( addr u -- )
+  0 ?do
+    dup i triangle-row-address @ . cr
+  loop drop ;
+
+: print-bell-row ( addr u -- )
+  tuck triangle-row-address swap
+  1+ 0 ?do
+    dup @ . cell+
+  loop drop cr ;
+
+: main ( -- )
+  15 bell-triangle
+  ." First 15 Bell numbers:" cr
+  dup 15 print-bell-numbers cr
+  ." First 10 rows of the Bell triangle:" cr
+  10 0 do
+    dup i print-bell-row
+  loop
+  triangle-deallocate ;
+
+main
+bye

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

Task/Bell-numbers/Miranda/bell-numbers.miranda

@@ -0,0 +1,16 @@
+main :: [sys_message]
+main = [Stdout "First 15 and 50th Bell numbers:\n",
+        Stdout (lay [(rjustify 2 (show i)) ++ ": " ++ show (bell_numbers ! i)
+                    | i <- [1..15] ++ [50]]),
+        Stdout "\nFirst 10 rows of the Bell triangle:\n",
+        Stdout (lay [concat [rjustify 7 (show n) | n <- row]
+                    | row <- take 10 bell_triangle])
+       ]
+
+
+bell_numbers :: [num]
+bell_numbers = map last bell_triangle
+
+bell_triangle :: [[num]]
+bell_triangle = iterate bell_step [1]
+                where bell_step row = scan (+) (last row) row

Task/Bell-numbers/PARI-GP/bell-numbers.parigp

@@ -0,0 +1,4 @@
+genit(maxx=50)={bell=List();
+for(n=0,maxx,q=sum(k=0,n,stirling(n,k,2));
+listput(bell,q));bell}
+END

Task/Bell-numbers/Refal/bell-numbers.refal

@@ -0,0 +1,41 @@
+$ENTRY Go {
+    , <BellNumbers 50>: e.Bell (e.B50)
+    , <First 15 e.Bell>: (e.F15) e.Rest
+    = <Each (Show) e.F15>
+      <Show e.B50>
+      <Each (Prout) <BellTriangle 10>>;
+}
+
+Show {
+    (e.X) = <Prout <Symb e.X>>;
+};
+
+BellNumbers {
+    s.N, <BellTriangle s.N>: e.Rows = <Each (Head) e.Rows>;
+};
+
+BellTriangle {
+    s.N = <BellTriangle <Sub s.N 1> ((1))>;
+    0 e.T = e.T;
+    s.N e.Rs (e.R) = <BellTriangle <Sub s.N 1> e.Rs (e.R) (<BellStep e.R>)>;
+};
+
+BellStep {
+    e.Row, e.Row: e.X (e.Last) = <Rsum (e.Last) e.Row>;
+};
+
+Rsum {
+    (Acc e.Acc) = ;
+    (Acc e.Acc) (e.N) e.Ns, <Add (e.N) e.Acc>: e.N2 =
+        (e.N2) <Rsum (Acc e.N2) e.Ns>;
+    e.Ns = <Rsum (Acc 0) e.Ns>;
+};
+
+Each {
+    (e.F) = ;
+    (e.F) (e.X) e.Xs = (<Mu e.F e.X>) <Each (e.F) e.Xs>;
+};
+
+Head {
+    t.X e.Y = t.X;
+};

Task/Bell-numbers/SETL/bell-numbers.setl

@@ -0,0 +1,31 @@
+program bell_numbers;
+    print("First 15 and 50th Bell numbers:");
+    b := bell_nums(50);
+    loop for i in [1..15] with 50 do
+        print(lpad(str i, 2) + ": " + str b(i));
+    end loop;
+
+    print;
+    print("First 10 rows of the Bell triangle:");
+    loop for row in bell_triangle(10) do
+        print(+/[lpad(str n, 7) : n in row]);
+    end loop;
+
+    proc bell_nums(n);
+        tri := bell_triangle(n);
+        return [row(#row) : row in tri];
+    end proc;
+
+    proc bell_triangle(rows);
+        tri := [[1]];
+        loop for i in [2..rows] do
+            row := tri(#tri);
+            nextrow := [row(#row)];
+            loop for n in row do
+                nextrow with:= nextrow(#nextrow) + n;
+            end loop;
+            tri with:= nextrow;
+        end loop;
+        return tri;
+    end proc;
+end program;