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== Examples == | == Examples == | ||
The three possible results of Signum on a real argument are < | The three possible results of Signum on a real argument are <syntaxhighlight lang=apl inline>0</syntaxhighlight>, <syntaxhighlight lang=apl inline>1</syntaxhighlight>, and <syntaxhighlight lang=apl inline>¯1</syntaxhighlight>. | ||
< | <syntaxhighlight 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. | ||
< | <syntaxhighlight 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]]: | ||
< | <syntaxhighlight lang=apl> | ||
| 3j4 | | 3j4 | ||
5 | 5 | ||
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. | ||
< | <syntaxhighlight 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 < | The identity <syntaxhighlight lang=apl inline>×z</syntaxhighlight> {{←→}} <syntaxhighlight lang=apl inline>z÷|z</syntaxhighlight> holds only when <syntaxhighlight 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 <syntaxhighlight lang=apl inline>0÷0</syntaxhighlight> to be equal to <syntaxhighlight 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 == | ||
| Line 41: | Line 41: | ||
* [http://microapl.com/apl_help/ch_020_020_050.htm APLX] | * [http://microapl.com/apl_help/ch_020_020_050.htm APLX] | ||
* J [https://www.jsoftware.com/help/dictionary/d110.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/star NuVoc] | * J [https://www.jsoftware.com/help/dictionary/d110.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/star NuVoc] | ||
* [https://mlochbaum.github.io/BQN/doc/arithmetic.html#basic-arithmetic BQN] | |||
== References == | == References == | ||
<references /> | <references /> | ||
{{APL built-ins}}[[Category:Primitive functions]][[Category:Scalar monadic functions]] | {{APL built-ins}}[[Category:Primitive functions]][[Category:Scalar monadic functions]] | ||