×), Sign, Sign of, or Direction is a monadic scalar function which returns the sign of a real or complex number. That is, it returns 0 when given an argument of 0, and otherwise returns a number with magnitude 1 given by dividing the argument by its own magnitude.
The three possible results of Signum on a real argument are
× ¯3 0 5 ¯1 0 1
In dialects with complex numbers, Signum is a somewhat more complicated function, and may return any unit complex number.
× 3j4 0.6J0.8
| 3j4 5 3j4 ÷ | 3j4 0.6J0.8
The magnitude of the result for a non-zero argument is always 1.
| × 3j4 ¯2j1 6j¯7 1 1 1
Zero divided by zero
z÷|z holds only when
z is not zero in most APLs. In "Zero Divided by Zero", Eugene McDonnell gave this identity as a reason to define
0÷0 to be equal to
0. In J, which took McDonnell's suggestion, the identity always holds. Dyalog APL and NARS2000 allow the choosing division method though the default remains 1.