110 lines
2.7 KiB
Python
110 lines
2.7 KiB
Python
from itertools import count, chain, tee, islice, cycle
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from fractions import Fraction
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# infinite polynomial class
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class Poly:
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def __init__(self, gen = None):
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self.gen, self.source = (None, gen) if type(gen) is Poly \
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else (gen, None)
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def __iter__(self):
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# We're essentially tee'ing it everytime the iterator
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# is, well, iterated. This may be excessive.
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return Poly(self)
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def getsource(self):
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if self.gen == None:
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s = self.source
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s.getsource()
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(a,b) = tee(s.gen, 2)
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s.gen = a
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self.gen = b
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def next(self):
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self.getsource()
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return next(self.gen)
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__next__ = next
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# Overload "<<" as stream input operator. Hey, C++ does it.
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def __lshift__(self, a): self.gen = a
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# The other operators are pretty much what one would expect
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def __neg__(self): return Poly(-x for x in self)
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def __sub__(a, b): return a + (-b)
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def __rsub__(a, n):
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a = Poly(a)
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def gen():
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yield(n - next(a))
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for x in a: yield(-x)
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return Poly(gen())
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def __add__(a, b):
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if type(b) is Poly:
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return Poly(x + y for (x,y) in zip(a,b))
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a = Poly(a)
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def gen():
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yield(next(a) + b)
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for x in a: yield(x)
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return Poly(gen())
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def __radd__(a,b):
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return a + b
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def __mul__(a,b):
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if not type(b) is Poly:
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return Poly(x*b for x in a)
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def gen():
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s = Poly(cycle([0]))
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for y in b:
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s += y*a
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yield(next(s))
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return Poly(gen())
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def __rmul__(a,b): return a*b
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def __truediv__(a,b):
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if not type(b) is Poly:
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return Poly(Fraction(x, b) for x in a)
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a, b = Poly(a), Poly(b)
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def gen():
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r, bb = a,next(b)
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while True:
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aa = next(r)
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q = Fraction(aa, bb)
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yield(q)
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r -= q*b
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return Poly(gen())
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# these two would probably be better as class methods
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def inte(a):
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def gen():
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yield(0)
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for (x,n) in zip(a, count(1)):
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yield(Fraction(x,n))
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return Poly(gen())
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def diff(a):
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def gen():
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for (x, n) in zip(a, count(0)):
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if n: yield(x*n)
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return Poly(gen())
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# all that for the syntactic sugar
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sinx, cosx, tanx, expx = Poly(), Poly(), Poly(), Poly()
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sinx << inte(cosx)
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cosx << 1 - inte(sinx)
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tanx << sinx / cosx # "=" would also work here
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expx << 1 + inte(expx)
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for n,x in zip(("sin", "cos", "tan", "exp"), (sinx, cosx, tanx, expx)):
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print(n, ', '.join(map(str, list(islice(x, 10)))))
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