On Thu, 10 Oct 2013 09:09:42 -0400, Roy Smith wrote: > BTW, here's a Python equality oddity: > >>>> r = 0.0 >>>> c = 0 + 0j >>>> r == c > True
Mathematically, this is only to be expected. >>>> int(r) == int(c) > Traceback (most recent call last): > File "<stdin>", line 1, in <module> > TypeError: can't convert complex to int This is also to be expected. What should int(a+bj) return? ★ int(a) + int(b)j ★ int(a) ★ int(b) ★ int(abs(a + bj)) It's quite ambiguous, there is no obvious mapping from complex to integers, and so should raise an exception. > If x == y, then f(x) should also equal f(y). Not necessarily. If x and y are different types, which they are here, then function f may be defined on one type but not the other. Which is exactly the case with int() on floats and complexes. > More specifically, if x == y, > and x is in the domain of f(), then y should also be in the domain of > f(). Incorrect. By definition, complex numbers are in the Complex domain, not the Real domain. Your mistake here seems to be that you're assuming that if two numbers are equal, they must be in the same domain, but that's not the case. (Perhaps you think that 0.0 == 0+0j should return False?) It's certainly not the case when it comes to types in Python, and it's not even the case in mathematics. Given: x ∈ ℝ, x = 2 (reals) y ∈ ℕ, y = 2 (natural numbers) we have x = y, but since 1/y is undefined (there is no Natural number 1/2), 1/x != 1/y. Now, arguably in this case we could implicitly promote y to the reals before performing the division. I would consider that acceptable, since there is only one way to do the promotion: natural 2 -> real 2. But going the other way certainly isn't: demoting real x to the naturals is ambiguous, and even if it weren't, then declaring that 1/x isn't defined would make the whole exercise pointless. Bringing this back to the initial example of int(0.0) == int(0+0j), to have this work the way you want would require demoting the complex number to the reals, and that is ambiguous. There are three distinct ways to do this: take the real part, the imaginary part, or the absolute value. That makes the operation "demote to real" ambiguous, the mere fact that all three operations would happen to give the same result for this particular number is irrelevant. -- Steven -- https://mail.python.org/mailman/listinfo/python-list
