Another update from ingydotnet^djgoku

Task/Paraffins/Haskell/paraffins-1.hs

@@ -0,0 +1,44 @@
+-- polynomial utils
+a `nmul` n = map (*n) a
+a `ndiv` n = map (`div` n) a
+
+instance (Integral a) => Num [a] where
+  (+) = zipWith (+)
+  negate = map negate
+  a * b = foldr f undefined b where
+    f x z = (a `nmul` x) + (0 : z)
+  abs _ = undefined
+  signum _ = undefined
+  fromInteger n = fromInteger n : repeat 0
+
+-- replace x in polynomial with x^n
+repl a n = concatMap (: replicate (n-1) 0) a
+
+-- S2: (a^2 + b)/2
+cycleIndexS2 a b = (a*a + b)`ndiv` 2
+
+-- S4: (a^4 + 6 a^2 b + 8 a c + 3 b^2 + 6 d) / 24
+cycleIndexS4 a b c d =	((a ^ 4) +
+			 (a ^ 2 * b) `nmul` 6 +
+			 (a * c) `nmul` 8 +
+			 (b ^ 2) `nmul` 3 +
+			 d `nmul` 6) `ndiv` 24
+
+
+a598 = x1
+-- A000598: A(x) = 1 + (1/6)*x*(A(x)^3 + 3*A(x)*A(x^2) + 2*A(x^3))
+x1 = 1 : ((x1^3) + ((x2*x1)`nmul` 3) + (x3`nmul`2)) `ndiv` 6
+x2 = x1`repl`2
+x3 = x1`repl`3
+x4 = x1`repl`4
+
+-- A000678 = x CycleIndex(S4, A000598(x))
+a678 = 0 : cycleIndexS4 x1 x2 x3 x4
+
+-- A000599 = CycleIndex(S2, A000598(x) - 1)
+a599 = cycleIndexS2 (0 : tail x1) (0 : tail x2)
+
+-- A000602 = A000678(x) - A000599(x) + A000599(x^2)
+a602 = a678 - a599 + x2
+
+main = mapM_ print $ take 200 $ zip [0 ..] a602

Task/Paraffins/Python/paraffins-2.py

@@ -0,0 +1,113 @@
+from itertools import count, chain, tee, islice, cycle
+from fractions import Fraction
+from sys import setrecursionlimit
+setrecursionlimit(5000)
+
+def frac(a,b): return a//b if a%b == 0 else Fraction(a,b)
+
+# infinite polynomial class
+class Poly:
+    def __init__(self, gen = None):
+        self.gen, self.source = (None, gen) if type(gen) is Poly \
+            else (gen, None)
+
+    def __iter__(self):
+        # We're essentially tee'ing it everytime the iterator
+        # is, well, iterated.  This may be excessive.
+        return Poly(self)
+
+    def getsource(self):
+        if self.gen == None:
+            s = self.source
+            s.getsource()
+            s.gen, self.gen = tee(s.gen, 2)
+
+    def next(self):
+        self.getsource()
+        return next(self.gen)
+
+    __next__ = next
+
+    # Overload "<<" as stream input operator. Hey, C++ does it.
+    def __lshift__(self, a): self.gen = a
+
+    # The other operators are pretty much what one would expect
+    def __neg__(self): return Poly(-x for x in self)
+
+    def __sub__(a, b): return a + (-b)
+
+    def __rsub__(a, n):
+        a = Poly(a)
+        def gen():
+            yield(n - next(a))
+            for x in a: yield(-x)
+        return Poly(gen())
+
+    def __add__(a, b):
+        if type(b) is Poly:
+            return Poly(x + y for (x,y) in zip(a,b))
+
+        a = Poly(a)
+        def gen():
+            yield(next(a) + b)
+            for x in a: yield(x)
+
+        return Poly(gen())
+
+    def __radd__(a,b):
+        return a + b
+
+    def __mul__(a,b):
+        if not type(b) is Poly:
+            return Poly(x*b for x in a)
+
+        def gen():
+            s = Poly(cycle([0]))
+            for y in b:
+                s += y*a
+                yield(next(s))
+
+        return Poly(gen())
+
+    def __rmul__(a,b): return a*b
+
+    def __truediv__(a,b):
+        if not type(b) is Poly:
+            return Poly(frac(x, b) for x in a)
+
+        a, b = Poly(a), Poly(b)
+        def gen():
+            r, bb = a,next(b)
+            while True:
+                aa = next(r)
+                q = frac(aa, bb)
+                yield(q)
+                r -= q*b
+
+        return Poly(gen())
+
+    def repl(self, n):
+        def gen():
+            for x in self:
+                yield(x)
+                for i in range(n-1): yield(0)
+        return Poly(gen())
+
+    def __pow__(self, n):
+        return Poly(self) if n == 1 else self * self**(n-1)
+
+def S2(a,b): return (a*a + b)/2
+def S4(a,b,c,d): return a**4/24 + a**2*b/4 + a*c/3 + b**2/8 + d/4
+
+x1 = Poly()
+x2 = x1.repl(2)
+x3 = x1.repl(3)
+x4 = x1.repl(4)
+x1 << chain([1], (x1**3 + 3*x1*x2 + 2*x3)/6)
+
+a598 = x1
+a678 = Poly(chain([0], S4(x1, x2, x3, x4)))
+a599 = S2(x1 - 1, x2 - 1)
+a602 = a678 - a599 + x2
+
+for n,x in zip(count(0), islice(a602, 500)): print(n,x)