Reciprocal
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÷

Reciprocal (÷
) is a monadic scalar function which gives the multiplicative inverse of a real or complex number. Reciprocal shares the glyph ÷
with the dyadic arithmetic function Divide.
Examples
÷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
Properties
The reciprocal of any real or complex number is equal to 1 divided by that number. Therefore the monadic ÷
can be seen as dyadic ÷
with default left argument of 1. This applies even to the reciprocal of 0; ÷0
and 1÷0
show identical behavior for both ⎕DIV←0
(raising DOMAIN ERROR) and ⎕DIV←1
(returning 0).
÷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
For any nonzero 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.
(×∘÷ ≡ +∘×)1 2 3 ¯2 0.5 1J2
1
(∘÷ ≡ ÷∘)1 2 3 ¯2 0.5 1J2
1
Works in: Dyalog APL