alt Hacker NewsThat's not what it simplifies to using a real or complex number domains for x, it's abs(x). CAS need type inference assumptions and/or type qualifiers to be more powerful.
Edit: Fixed stuff.
Replies
fph • today at 12:46 PM
It's abs(x) only over the reals, for complex numbers it's more complicated.
SoftTalker • today at 4:40 PM
That abs(x) (or |x| as we wrote it) used to catch out so many of us in HS trig and algebra.
jstanley • today at 8:56 AM
Right, that's why you need further assumptions on x in order for that simplification to hold.
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For x = -i, square(x) = -1, sqrt(square(x)) = i. Meanwhile, abs(x) = 1. You're right that it simplifies to abs(x) for real x, but that no longer holds for arbitrary complex values.