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Reciprocal: Difference between revisions
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{{Built-in|Reciprocal|÷}} is a [[monadic]] [[scalar function]] which gives the [[wikipedia:Multiplicative inverse|multiplicative inverse]] of a real or [[complex]] number. Reciprocal shares the [[glyph]] <syntaxhighlight lang=apl inline>÷</ | {{Built-in|Reciprocal|÷}} is a [[monadic]] [[scalar function]] which gives the [[wikipedia:Multiplicative inverse|multiplicative inverse]] of a real or [[complex]] number. Reciprocal shares the [[glyph]] <syntaxhighlight lang=apl inline>÷</syntaxhighlight> with the dyadic arithmetic function [[Divide]]. | ||
== Examples == | == Examples == | ||
| Line 17: | Line 17: | ||
÷0 | ÷0 | ||
0 | 0 | ||
</ | </syntaxhighlight> | ||
== Properties == | == Properties == | ||
The reciprocal of any real or complex number is equal to 1 [[divide]]d by that number. Therefore the monadic <syntaxhighlight lang=apl inline>÷</ | The reciprocal of any real or complex number is equal to 1 [[divide]]d by that number. Therefore the monadic <syntaxhighlight lang=apl inline>÷</syntaxhighlight> can be seen as dyadic <syntaxhighlight lang=apl inline>÷</syntaxhighlight> with default left argument of 1. This applies even to the reciprocal of 0; <syntaxhighlight lang=apl inline>÷0</syntaxhighlight> and <syntaxhighlight lang=apl inline>1÷0</syntaxhighlight> show identical behavior for both <syntaxhighlight lang=apl inline>⎕DIV←0</syntaxhighlight> (raising [[DOMAIN ERROR]]) and <syntaxhighlight lang=apl inline>⎕DIV←1</syntaxhighlight> (returning 0). | ||
<syntaxhighlight lang=apl> | <syntaxhighlight lang=apl> | ||
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1÷1 2 3 4 5 | 1÷1 2 3 4 5 | ||
1 0.5 0.3333333333 0.25 0.2 | 1 0.5 0.3333333333 0.25 0.2 | ||
</ | </syntaxhighlight> | ||
For any non-zero real or complex numbers, the [[signum]] of reciprocal is equal to the [[conjugate]] of signum, and the [[magnitude]] of reciprocal is equal to the reciprocal of magnitude. | For any non-zero real or complex numbers, the [[signum]] of reciprocal is equal to the [[conjugate]] of signum, and the [[magnitude]] of reciprocal is equal to the reciprocal of magnitude. | ||
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(|∘÷ ≡ ÷∘|)1 2 3 ¯2 0.5 1J2 | (|∘÷ ≡ ÷∘|)1 2 3 ¯2 0.5 1J2 | ||
1 | 1 | ||
</ | </syntaxhighlight>{{Works in|[[Dyalog APL]]}} | ||
== See also == | == See also == | ||