 |
The sign of a real number, also called sgn or signum, is 
for a negative number (i.e.,
one with a minus sign "
"), 0 for the number zero, or
for a positive
number (i.e., one with a plus sign "
"). In other words, for real 
,
 |
(1)
|
For real 
, this can be written
 |
(2)
|
and satisfies
 |
(3)
|
for real 
can also be defined as
 |
(4)
|
where 
is the Heaviside
step function.
The sign function is implemented in the Wolfram Language for real 
as Sign[x].
For nonzero complex numbers, Sign[z]
returns 
, where 
is the complex modulus
of 
.
can also be interpreted as an unspecified
point on the unit circle in the complex plane (Rich and Jeffrey 1996).
." In