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 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.
(×∘÷ ≡ +∘×)1 2 3 ¯2 0.5 1J2
1
(|∘÷ ≡ ÷∘|)1 2 3 ¯2 0.5 1J2
1
Works in: Dyalog APL