Initial data commit

Task/Faulhabers-formula/Python/faulhabers-formula.py

@@ -0,0 +1,63 @@
+from fractions import Fraction
+
+def nextu(a):
+    n = len(a)
+    a.append(1)
+    for i in range(n - 1, 0, -1):
+        a[i] = i * a[i] + a[i - 1]
+    return a
+
+def nextv(a):
+    n = len(a) - 1
+    b = [(1 - n) * x for x in a]
+    b.append(1)
+    for i in range(n):
+        b[i + 1] += a[i]
+    return b
+
+def sumpol(n):
+    u = [0, 1]
+    v = [[1], [1, 1]]
+    yield [Fraction(0), Fraction(1)]
+    for i in range(1, n):
+        v.append(nextv(v[-1]))
+        t = [0] * (i + 2)
+        p = 1
+        for j, r in enumerate(u):
+            r = Fraction(r, j + 1)
+            for k, s in enumerate(v[j + 1]):
+                t[k] += r * s
+        yield t
+        u = nextu(u)
+
+def polstr(a):
+    s = ""
+    q = False
+    n = len(a) - 1
+    for i, x in enumerate(reversed(a)):
+        i = n - i
+        if i < 2:
+            m = "n" if i == 1 else ""
+        else:
+            m = "n^%d" % i
+        c = str(abs(x))
+        if i > 0:
+            if c == "1":
+                c = ""
+            else:
+                m = " " + m
+        if x != 0:
+            if q:
+                t = " + " if x > 0 else " - "
+                s += "%s%s%s" % (t, c, m)
+            else:
+                t = "" if x > 0 else "-"
+                s = "%s%s%s" % (t, c, m)
+                q = True
+    if q:
+        return s
+    else:
+        return "0"
+
+for i, p in enumerate(sumpol(10)):
+    print(i, ":", polstr(p))