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]
Primitive functions
Scalar
Monadic ConjugateNegateSignumReciprocalMagnitudeExponentialNatural LogarithmFloorCeilingFactorialNotPi TimesRollTypeImaginarySquare Root
Dyadic AddSubtractTimesDivideResiduePowerLogarithmMinimumMaximumBinomialComparison functionsBoolean functions (And, Or, Nand, Nor) ∙ GCDLCMCircularComplexRoot
Non-Scalar
Structural ShapeReshapeTallyDepthRavelEnlistTableCatenateReverseRotateTransposeRazeMixSplitEncloseNestCut (K)PairLinkPartitioned EnclosePartition
Selection FirstPickTakeDropUniqueIdentitySelectReplicateExpandSet functions (IntersectionUnionWithout) ∙ Bracket indexingIndex
Selector Index generatorGradeIndex OfInterval IndexIndicesDeal
Computational MatchNot MatchMembershipFindNub SieveEncodeDecodeMatrix InverseMatrix DivideFormatExecuteMaterialiseRange
Primitive operators Monadic EachCommuteConstantReplicateExpandReduceWindowed ReduceScanOuter ProductKeyI-BeamSpawnFunction axis
Dyadic BindCompositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner ProductPowerAtUnderRankDepthVariantStencilCut (J)
Quad names
Arrays Index originMigration levelAtomic vector
Functions Name classCase convertUnicode convert
Operators SearchReplace