Difference between revisions of "Signum"
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−  {{BuiltinSignum×}}, '''Sign''', '''Sign of''', or '''Direction''' is a [[monadic]] [[  +  {{BuiltinSignum×}}, '''Sign''', '''Sign of''', or '''Direction''' is a [[monadic]] [[scalar function]] which returns the [[wikipedia:Sign functionsign]] 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 [[Dividedividing]] the argument by its own magnitude. 
== Examples ==  == Examples == 
Revision as of 23:40, 28 May 2020
×

Signum (×
), 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.
Examples
The three possible results of Signum on a real argument are 0
, 1
, and ¯1
.
× ¯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
The result is still equal to the original number divided by its magnitude:
 3j4
5
3j4 ÷  3j4
0.6J0.8
The magnitude of the result for a nonzero argument is always 1.
 × 3j4 ¯2j1 6j¯7
1 1 1
Zero divided by zero
The identity ×z
z÷z
holds only when z
is not zero in most APLs. In "Zero Divided by Zero"^{[1]}, 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.