Signum: Difference between revisions
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== Examples == | == Examples == | ||
The three possible results of Signum on a real argument are <source lang=apl inline>0</ | The three possible results of Signum on a real argument are <source lang=apl inline>0</syntaxhighlight>, <source lang=apl inline>1</syntaxhighlight>, and <source lang=apl inline>¯1</syntaxhighlight>. | ||
<source lang=apl> | <source lang=apl> | ||
× ¯3 0 5 | × ¯3 0 5 | ||
¯1 0 1 | ¯1 0 1 | ||
</ | </syntaxhighlight> | ||
In dialects with [[complex number]]s, Signum is a somewhat more complicated function, and may return any unit complex number. | In dialects with [[complex number]]s, Signum is a somewhat more complicated function, and may return any unit complex number. | ||
<source lang=apl> | <source lang=apl> | ||
× 3j4 | × 3j4 | ||
0.6J0.8 | 0.6J0.8 | ||
</ | </syntaxhighlight> | ||
The result is still equal to the original number [[divide]]d by its [[magnitude]]: | The result is still equal to the original number [[divide]]d by its [[magnitude]]: | ||
<source lang=apl> | <source lang=apl> | ||
| Line 19: | Line 19: | ||
3j4 ÷ | 3j4 | 3j4 ÷ | 3j4 | ||
0.6J0.8 | 0.6J0.8 | ||
</ | </syntaxhighlight> | ||
The [[magnitude]] of the result for a non-zero argument is always 1. | The [[magnitude]] of the result for a non-zero argument is always 1. | ||
<source lang=apl> | <source lang=apl> | ||
| × 3j4 ¯2j1 6j¯7 | | × 3j4 ¯2j1 6j¯7 | ||
1 1 1 | 1 1 1 | ||
</ | </syntaxhighlight> | ||
== Zero divided by zero == | == Zero divided by zero == | ||
The identity <source lang=apl inline>×z</ | The identity <source lang=apl inline>×z</syntaxhighlight> {{←→}} <source lang=apl inline>z÷|z</syntaxhighlight> holds only when <source lang=apl inline>z</syntaxhighlight> 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</syntaxhighlight> to be equal to <source lang=apl inline>0</syntaxhighlight>. In [[J]], which took McDonnell's suggestion, the identity always holds. [[Dyalog APL]] and [[NARS2000]] allow choosing [[division method]] though the default remains 1. | ||
== See also == | == See also == | ||
Revision as of 21:07, 10 September 2022
×
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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 <source lang=apl inline>0</syntaxhighlight>, <source lang=apl inline>1</syntaxhighlight>, and <source lang=apl inline>¯1</syntaxhighlight>. <source lang=apl>
× ¯3 0 5
¯1 0 1 </syntaxhighlight> In dialects with complex numbers, Signum is a somewhat more complicated function, and may return any unit complex number. <source lang=apl>
× 3j4
0.6J0.8 </syntaxhighlight> The result is still equal to the original number divided by its magnitude: <source lang=apl>
| 3j4
5
3j4 ÷ | 3j4
0.6J0.8 </syntaxhighlight> The magnitude of the result for a non-zero argument is always 1. <source lang=apl>
| × 3j4 ¯2j1 6j¯7
1 1 1 </syntaxhighlight>
Zero divided by zero
The identity <source lang=apl inline>×z</syntaxhighlight> <source lang=apl inline>z÷|z</syntaxhighlight> holds only when <source lang=apl inline>z</syntaxhighlight> is not zero in most APLs. In "Zero Divided by Zero"[1], Eugene McDonnell gave this identity as a reason to define <source lang=apl inline>0÷0</syntaxhighlight> to be equal to <source lang=apl inline>0</syntaxhighlight>. In J, which took McDonnell's suggestion, the identity always holds. Dyalog APL and NARS2000 allow choosing division method though the default remains 1.
See also
External links
Documentation
- Dyalog
- APLX
- J Dictionary, NuVoc
- BQN