Exponential

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This page describes the monadic arithmetic function. For the dyadic function, see Power (function).
*

Exponential (*) is a monadic scalar function which computes the exponential function (i.e. the power of Euler's constant e) of the argument. Exponential shares the glyph <source lang=apl inline>*</syntaxhighlight> with the dyadic arithmetic function Power.

Examples

Euler's constant itself can be obtained by supplying 1 as the argument.

<source lang=apl> 

     *1

2.718281828 </syntaxhighlight>

On APL implementations that support complex numbers, one can demonstrate Euler's identity (with the help of Pi Times <source lang=apl inline>○</syntaxhighlight>):

<source lang=apl> 

     1+*○0J1

0

</syntaxhighlight>

Works in: Dyalog APL

Properties

Exponential is a special case of Power with the default left argument of e (<source lang=apl inline>*1</syntaxhighlight>).

<source lang=apl> 

     ((*1)∘* ≡ *) 0 1 ¯1 0J1

1

</syntaxhighlight>

Works in: Dyalog APL

Exponential and natural log <source lang=apl inline>⍟</syntaxhighlight> are inverses of each other, except where the natural log is undefined.

<source lang=apl> 

     (⊢ ≡ ⍟∘*) 0 1 ¯1 0J1

1 

     (⊢ ≡ *∘⍟) 1 ¯1 0J1 ⍝ natural log of zero is undefined

1

</syntaxhighlight>

Works in: Dyalog APL

See also

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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