# Reciprocal: Difference between revisions

 `÷`

Reciprocal (`÷`) is a monadic scalar function which gives the multiplicative inverse of a real or complex number. Reciprocal shares the glyph <syntaxhighlight lang=apl inline>÷</source> with the dyadic arithmetic function Divide.

## Examples

<syntaxhighlight lang=apl>

```     ÷1 2 3 4 5
```

1 0.5 0.3333333333 0.25 0.2

```     ÷¯2 0.5 1J2
```

¯0.5 2 0.2J¯0.4

```     ÷0
```

DOMAIN ERROR: Divide by zero

```÷0
∧

⎕DIV←1  ⍝ this sets division by 0 to always return 0
÷0
```

0 </source>

## Properties

The reciprocal of any real or complex number is equal to 1 divided by that number. Therefore the monadic <syntaxhighlight lang=apl inline>÷</source> can be seen as dyadic <syntaxhighlight lang=apl inline>÷</source> with default left argument of 1. This applies even to the reciprocal of 0; <syntaxhighlight lang=apl inline>÷0</source> and <syntaxhighlight lang=apl inline>1÷0</source> show identical behavior for both <syntaxhighlight lang=apl inline>⎕DIV←0</source> (raising DOMAIN ERROR) and <syntaxhighlight lang=apl inline>⎕DIV←1</source> (returning 0).

<syntaxhighlight lang=apl>

```     ÷1 2 3 4 5
```

1 0.5 0.3333333333 0.25 0.2

```     1÷1 2 3 4 5
```

1 0.5 0.3333333333 0.25 0.2 </source>

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.

<syntaxhighlight lang=apl>

```     (×∘÷ ≡ +∘×)1 2 3 ¯2 0.5 1J2
```

1

```     (|∘÷ ≡ ÷∘|)1 2 3 ¯2 0.5 1J2
```

1

</source>

Works in: Dyalog APL