Another update from ingydotnet^djgoku

Task/Formal-power-series/Python/formal-power-series-3.py

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+from itertools import count, chain, tee, islice, cycle
+from fractions import Fraction
+
+# 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()
+            (a,b) = tee(s.gen, 2)
+            s.gen = a
+            self.gen = b
+
+    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(Fraction(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 = Fraction(aa, bb)
+                yield(q)
+                r -= q*b
+
+        return Poly(gen())
+
+# these two would probably be better as class methods
+def inte(a):
+    def gen():
+        yield(0)
+        for (x,n) in zip(a, count(1)):
+            yield(Fraction(x,n))
+    return Poly(gen())
+
+def diff(a):
+    def gen():
+        for (x, n) in zip(a, count(0)):
+            if n: yield(x*n)
+    return Poly(gen())
+
+
+# all that for the syntactic sugar
+sinx, cosx, tanx, expx = Poly(), Poly(), Poly(), Poly()
+
+sinx << inte(cosx)
+cosx << 1 - inte(sinx)
+tanx << sinx / cosx        # "=" would also work here
+expx << 1 + inte(expx)
+
+for n,x in zip(("sin", "cos", "tan", "exp"), (sinx, cosx, tanx, expx)):
+    print(n, ', '.join(map(str, list(islice(x, 10)))))