⁻ — Inverse

Monadic operator. Keys: Alt-_. Hanzi: 反

f⁻ is f⍣¯1. f⁻Y gives the X for which f X is Y. In a dyadic call, X f⁻Y keeps X fixed and finds the right argument Z for which X f Z is Y.

*⁻1           ⍝ 0
2×⁻10         ⍝ 5
(+↢3)⁻10      ⍝ 7

BPL infers inverses of the primitives and compositions listed under Power. f⁻←g attaches an inverse to a named function.

The minus is bare: no superscript digit follows it. f⁻¹ means Rank ¯1. f⁻ ¹ applies the inverse at rank 1. Numeric superscripts on arrays remain powers, including the reciprocal 2⁻¹.

⌽⁻ ¹[1 2⋄3 4]   ⍝ [2 1⋄4 3]

An inverse applies to the whole derived function on its left. Use parentheses or a space when that function ends in a number: (+↢3)⁻10 or +↢3 ⁻ 10.

Errors: DOMAIN for an unknown inverse or an array operand.