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== Zero divided by zero ==
== Zero divided by zero ==


The identity <source lang=apl inline>×z</source> {{←→}} <source lang=apl inline>z÷|z</source> holds only when <source lang=apl inline>z</source> is not zero in most APLs. In "Zero Divided by Zero"<ref>[[Eugene McDonnell|McDonnell, Eugene]]. [https://www.jsoftware.com/papers/eem/0div0.htm "Zero Divided by Zero"]. [[APL76]].</ref>, [[Eugene McDonnell]] gave this identity as a reason to define <source lang=apl inline>0÷0</source> to be equal to <source lang=apl inline>0</source>. In [[J]], which took McDonnell's suggestion, the identity always holds.
The identity <source lang=apl inline>×z</source> {{←→}} <source lang=apl inline>z÷|z</source> holds only when <source lang=apl inline>z</source> is not zero in most APLs. In "Zero Divided by Zero"<ref>[[Eugene McDonnell|McDonnell, Eugene]]. [https://www.jsoftware.com/papers/eem/0div0.htm "Zero Divided by Zero"]. [[APL76]].</ref>, [[Eugene McDonnell]] gave this identity as a reason to define <source lang=apl inline>0÷0</source> to be equal to <source lang=apl inline>0</source>. 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.


== External links ==
== External links ==

Revision as of 15:13, 27 March 2020

×

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. Dyalog APL and NARS2000 allow the choosing division method though the default remains 1.

External links

Documentation

References

  1. ↑ McDonnell, Eugene. "Zero Divided by Zero". APL76.
APL built-ins [edit]
Primitives (Timeline) Functions
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