 This page describes the dyadic function. For the monadic function that uses $e$ 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 nth 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 builtins [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

NonScalar

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 ∙ IBeam ∙ Spawn ∙ Function axis ∙ Identity (Null, Ident)

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
