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That'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.

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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.

Right, that's why you need further assumptions on x in order for that simplification to hold.

It's not a simplification, it's wrong. Sqrt(square(x)) equals abs(x).

It also equals x with appropriate assumptions (x > 0).

Well, then sin(x) = x if x is infinitely small

so there's an unconditionally correct answer (it's also equal to abs(x) for x>0), and then there is an answer that is only correct for half the domain, which requires an additional assumption.



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