Power (function): Difference between revisions

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(Created page with ":''This page describes the dyadic arithmetic function. For the monadic natural exponential function (power of e), see Exponential. For the operator that iterates the funct...")
 
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       2*¯1 0 1 2 3 4 5
       2*¯1 0 1 2 3 4 5
0.5 1 2 4 8 16 32
0.5 1 2 4 8 16 32
</source>
A common technique is to choose [[sign]] based on [[Boolean]]s:
<source lang=apl>
      ¯1*1 0 0 1 0
¯1 1 1 ¯1 1
</source>
</source>


Revision as of 05:23, 2 June 2020

This page describes the dyadic arithmetic function. For the monadic natural exponential function (power of e), see Exponential. For the operator that iterates the function operand, see Power (operator).
*

Power (*) is a dyadic scalar function which computes the exponentiation function of the two arguments. More precisely, X*Y computes X raised to the power of 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 Booleans: 

      ¯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

Negation on the power results in the reciprocal on the return value. 

      (2*¯4)=÷2*4
1

Reciprocal on the power results in the n-th root on the return value. This can be used to calculate the square root. 

      3*2
9
      9*÷2
3

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)
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
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