Power (function)

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This page describes the dyadic function. For the monadic function that uses as a base, see Exponential. For the iteration operator, see Power (operator).
*

Power (*) is a dyadic scalar function that computes the exponentiation function of the two arguments, so that X*Y is X raised to the power Y. Power shares the glyph * with the monadic arithmetic function Exponential.

Examples

      2*¯1 0 1 2 3 4 5
0.5 1 2 4 8 16 32

A common technique is to choose sign based on a Boolean array: 

      ¯1*1 0 0 1 0
¯1 1 1 ¯1 1

Properties

For positive integer Y, X*Y equals the product of Y copies of X. When Y is 0, X*Y equals 1, possibly except when X is also 0 (since zero to the power of zero is undefined in mathematics). 

      3*5
243 
      ×/5⍴3
243
      1 2 3*0
1 1 1

Negating the exponent (right argument) gives the reciprocal of the return value. 

      (2*¯4)=÷2*4
1

If the exponent is the reciprocal of some number n, the result is the n-th root of the base. For example, a right argument of ÷2 gives the square root. 

      3*2
9
      9*÷2
3

Power has two inverses, Root and Logarithm: 

      2*3
8
      2⍟8
3
      3√8
2

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
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
Dyadic Bind ∙ Compositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner Product ∙ Determinant ∙ Power ∙ At ∙ Under ∙ Rank ∙ Depth ∙ Variant ∙ Stencil ∙ Cut ∙ Direct definition (operator)
Quad names Index origin ∙ Comparison tolerance ∙ Migration level ∙ Atomic vector
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