#4922 sign(complex^2) = pz, sign(imaginary^2) = pz

[David Scherfgen]

• With z declared complex, sign(z^2) gives pz. Shouldn't it be pnz?
• With j declared imaginary, sign(j^2) gives pz. Shouldn't it be nz?

(csign answers correctly.)

The documentation for sign says:

Note that this function assumes that expr is a real-valued expression

But should it also assume this when the user explicitly declared something as complex or imaginary?

[Stavros Macrakis]

Since sign is clearly documented as assuming that its argument is a real-valued expression, I would argue that as soon as it sees anything explicitly complex, it should raise an error, even if the overall value of the expression is real.

That is, all the following cases should raise an error:

sign(%i) << already gives error
sign(z)
sign(z^2)
sign(j^2)
sign(abs(x+%i))
sign((x+%i)*(x-%i)) => pos (because it expands)

The error should be something like
:The sign function is only defined for expressions not involving complex quantities.

The rationale is that if it acts as though it works on any complex quantities, users will have the reasonable expectation that it will work in general with complex quantities, such as sqrt(x), log(x), asin(x), ....

After all, sign(sqrt(x)) doesn't even ask whether whether x is negative.