This is a general pattern in CAS. For a more basic case, it’s not obvious sqrt(square(x)) will simplify to x without any further assumptions on x.

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burnt-resistor 3 hours ago | parent [-]

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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yorwba an hour ago | parent | next [-]

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.

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jstanley 3 hours ago | parent | prev [-]

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

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contubernio 3 hours ago | parent [-]

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

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MForster 2 hours ago | parent [-]

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

	▲	notarget137 11 minutes ago \| parent \| next [-]
		Well, then sin(x) = x if x is infinitely small
	▲	exe34 43 minutes ago \| parent \| prev [-]
		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.