Reciprocal

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

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

External links

Documentation

APL built-ins [edit]
Primitives (Timeline)	Functions
Scalar
		Monadic	Conjugate ∙ Negate ∙ Signum ∙ Reciprocal ∙ Magnitude ∙ Exponential ∙ Natural Logarithm ∙ Floor ∙ Ceiling ∙ Factorial ∙ Not ∙ Pi Times ∙ Roll ∙ Type ∙ Imaginary ∙ Square Root ∙ Round
		Dyadic	Add ∙ Subtract ∙ Times ∙ Divide ∙ Residue ∙ Power ∙ Logarithm ∙ Minimum ∙ Maximum ∙ Binomial ∙ Comparison functions ∙ Boolean functions (And, Or, Nand, Nor) ∙ GCD ∙ LCM ∙ Circular ∙ Complex ∙ Root
Non-Scalar
		Structural	Shape ∙ Reshape ∙ Tally ∙ Depth ∙ Ravel ∙ Enlist ∙ Table ∙ Catenate ∙ Reverse ∙ Rotate ∙ Transpose ∙ Raze ∙ Mix ∙ Split ∙ Enclose ∙ Nest ∙ Cut (K) ∙ Pair ∙ Link ∙ Partitioned Enclose ∙ Partition
		Selection	First ∙ Pick ∙ Take ∙ Drop ∙ Unique ∙ Identity ∙ Stop ∙ Select ∙ Replicate ∙ Expand ∙ Set functions (Intersection ∙ Union ∙ Without) ∙ Bracket indexing ∙ Index ∙ Cartesian Product ∙ Sort
		Selector	Index generator ∙ Grade ∙ Index Of ∙ Interval Index ∙ Indices ∙ Deal ∙ Prefix and suffix vectors
		Computational	Match ∙ Not Match ∙ Membership ∙ Find ∙ Nub Sieve ∙ Encode ∙ Decode ∙ Matrix Inverse ∙ Matrix Divide ∙ Format ∙ Execute ∙ Materialise ∙ Range
Operators	Monadic	Each ∙ Commute ∙ Constant ∙ Replicate ∙ Expand ∙ Reduce ∙ Windowed Reduce ∙ Scan ∙ Outer Product ∙ Key ∙ I-Beam ∙ Spawn ∙ Function axis ∙ Identity (Null, Ident)
Operators	Dyadic	Bind ∙ Compositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner Product ∙ Determinant ∙ Power ∙ At ∙ Under ∙ Rank ∙ Depth ∙ Variant ∙ Stencil ∙ Cut ∙ Direct definition (operator) ∙ Identity (Lev, Dex)
Quad names	Index origin ∙ Comparison tolerance ∙ Migration level ∙ Atomic vector

Reciprocal

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Reciprocal

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