Signum

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Signum (×), Sign, Sign of, or Direction is a monadic primitive 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 non-zero 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.

External links

Documentation

References

  1. ↑ McDonnell, Eugene. "Zero Divided by Zero". APL76.
APL built-ins [edit]
Primitives (Timeline) Functions
Scalar
Monadic Conjugate ∙ Negate ∙ Signum ∙ Reciprocal ∙ Magnitude ∙ Exponential ∙ Natural Logarithm ∙ Floor ∙ Ceiling ∙ Factorial ∙ Not ∙ Pi Times ∙ Roll ∙ Type ∙ Imaginary ∙ Square Root ∙ Round
Dyadic Add ∙ Subtract ∙ Times ∙ Divide ∙ Residue ∙ Power ∙ Logarithm ∙ Minimum ∙ Maximum ∙ Binomial ∙ Comparison functions ∙ Boolean functions (And, Or, Nand, Nor) ∙ GCD ∙ LCM ∙ Circular ∙ Complex ∙ Root
Non-Scalar
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Selector Index generator ∙ Grade ∙ Index Of ∙ Interval Index ∙ Indices ∙ Deal ∙ Prefix and suffix vectors
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Operators Monadic Each ∙ Commute ∙ Constant ∙ Replicate ∙ Expand ∙ Reduce ∙ Windowed Reduce ∙ Scan ∙ Outer Product ∙ Key ∙ I-Beam ∙ Spawn ∙ Function axis ∙ Identity (Null, Ident)
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Quad names Index origin ∙ Comparison tolerance ∙ Migration level ∙ Atomic vector
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