Exponential

From APL Wiki
Jump to navigation Jump to search
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.
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 * with the dyadic arithmetic function Power.

Examples

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

      *1
2.718281828

On APL implementations that support complex numbers, one can demonstrate Euler's identity (with the help of Pi Times ):

      1+*○0J1
0
Works in: Dyalog APL

Properties

Exponential is a special case of Power with the default left argument of e (*1).

      ((*1)*  *) 0 1 ¯1 0J1
1
Works in: Dyalog APL

Exponential and natural log are inverses of each other, except where the natural log is undefined.

      (  *) 0 1 ¯1 0J1
1
      (  *) 1 ¯1 0J1 ⍝ natural log of zero is undefined
1
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