If we wanted to be mathematically correct, taking a 4th root should give you 4 answers. You could return a tuple of (4, -4, 4j, -4j) for a 4th root of 256. It actually makes power to a Fraction(2, 4) unequal with a Fraction(1, 2) calculating this way. (which, from what I can tell, is exactly your point - don't just take a power and a square root for a fractional power, reduce it to a float or whatever first to get well-defined behaviour. ) But full mathematical correctness is probably not what we want either. Current behaviour IMO is the only solution that returns only 1 answer but does something sensible in all cases. Op za 1 sep. 2018 om 20:35 schreef Jonathan Fine <jfine2358@gmail.com>:
Greg Ewing and Jonathan Goble wrote
Also, Fraction(1) for the second case would be flat-out wrong.
How? Raising something to the 2/3 power means squaring it and then taking the cube root of it. -1 squared is 1, and the cube root of 1 is 1. Or am I having a 2:30am brain fart?
Let's see. What about computing the Fraction(2, 4) power by first squaring and then taking the fourth root. Let's start with (-16). Square to get +256. And then the fourth root is +4. I've just followed process Jonathan G suggested, without noticing that Fraction(2, 4) is equal to Fraction(1, 2).
But Fraction(1, 2) is the square root. And -16 requires complex numbers for its square root. The problem, I think, may not be doing something sensible in any particular case. Rather, it could be doing something sensible and coherent in all cases. A bit like trying to fit a carpet that is cut to the wrong size for the room.
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