Comment #2 on issue 2852 by smi...@gmail.com: is_constant(wrt) is needed
http://code.google.com/p/sympy/issues/detail?id=2852
And even if we can't prove that something is zero at least we can know if
it's constant (see last example):
>>> def is_constant(self, *wrt):
... if self.is_Number or self.is_number:
... return True
... if not wrt:
... free = self.free_symbols
... if not free:
... return True
... # maybe false
... free =list(free)
... for i in range(len(free)):
... deriv = self.diff(free[0])
... if expand_mul(deriv) != 0 and not is_constant(deriv,
*free):
... return False
... free.pop(0)
... return True
... if not self.has(*wrt) or not set(wrt) & self.free_symbols:
... return True
... # maybe true
... return all(expand_mul(self.diff(v)) == 0 for v in wrt)
...
>>> is_constant(Sum(x, (x, 1, 10)))
True
>>> is_constant(Sum(x, (x, 1, n)))
False
>>> is_constant(Sum(x, (x, 1, n)), y)
True
>>> is_constant(Sum(x, (x, 1, n)), n)
False
>>> is_constant(Sum(x, (x, 1, n)), x)
True
>>> is_constant(a*cos(x)**2+a*sin(x)**2-a)
True
>>> is_constant(a*cos(x)**2+a*sin(x)**2-1)
True
>>> (a*cos(x)**2+a*sin(x)**2-a).is_zero
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