sgn
The sign (signum) function.
Syntax
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sgn(x)-
xis a real or complex number
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Description
For real x, sgn(x) is the sign of x:
⎧ −1 if x < 0
sgn(x) = ⎨ 0 if x = 0
⎩ +1 if x > 0.
Typewise, sgn(x) is an integer.
Clearly, for non-zero x,
sgn(x) = x/abs(x)
which motivates the definition of sgn(z) for complex z:
sgn(z) = z/abs(z) if z ≠ 0 sgn(0) = 0.
Typewise, sgn(z) is a complex number.
Examples
sgn(1 + i)
0.707106781187 + 0.707106781187⋅i
collapse(SequenceVector(1000) @ Mertens @ sgn)
(1, 1) (0, 1) (−1, 36) (0, 2) (−1, 17) (0, 1) (−1, 6) (0, 1) (−1, 27) (0, 1) (1, 7) ⋮