# Inverse

Revision as of 23:23, 29 January 2024 by Marshall (talk | contribs) (Created page with "The '''inverse''' of a function is a function that undoes its effect, computing an argument that corresponds to the given result for that function. In APL it's usually written with the Power operator as <syntaxhighlight lang=apl inline>(f⍣¯1) x</syntaxhighlight>. While some functions such as Reverse have an obvious exact inverse, others might have no valid inverse or many possible choices for a given result. Treatment of these cases varies among dialects, but...")

The **inverse** of a function is a function that undoes its effect, computing an argument that corresponds to the given result for that function. In APL it's usually written with the Power operator as `(f⍣¯1) x`

. While some functions such as Reverse have an obvious exact inverse, others might have no valid inverse or many possible choices for a given result. Treatment of these cases varies among dialects, but a common rule is that the inverse should satisfy `x ≡ f (f⍣¯1) x`

, making it a right inverse in mathematical terminology. A stand-alone inverse operator is defined in Kap (`˝`

), BQN ("Undo", `⁼`

), and Uiua ("Un", `°`

).

As with Power in general, the dyadic inverse `⍺(f⍣¯1)⍵`

is defined to be the inverse of `⍺∘f`

, that is, `(⍺∘f⍣¯1)⍵`

.

## External links

### Lessons

- APL Cultivation 34