Difference between revisions of "Imaginary"

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{{Built-in|Imaginary|⌾}} is a [[monadic]] [[scalar function]] which multiplies the [[argument]] by the imaginary unit <source lang=apl inline>0J1</source>. This can be seen as a mapping from a real number to a pure imaginary number (a [[complex number]] with the real part of 0). It was added to [[J]] as <source lang=j inline>j.</source> together with initial support for complex numbers, and was adopted in [[Extended Dyalog APL]] using the [[glyph]] <source lang=apl inline>⌾</source> as a monadic counterpart of [[Complex (function)|Complex]]. In other APL implementations that support complex numbers, [[Circular]] with the left argument of <source lang=apl inline>¯11</source> has the same functionality as Imaginary.
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{{Built-in|Imaginary|⌾}} is a [[monadic]] [[scalar function]] which multiplies the [[argument]] by the [[wikipedia:imaginary unit|imaginary unit]] <source lang=apl inline>0J1</source>, usually denoted <math>i</math> or <math>j</math> in traditional mathematics. This can be seen as a mapping from a real number to a pure imaginary number (a [[complex number]] with the real part of 0). It was added to [[J]] as <source lang=j inline>j.</source> together with initial support for complex numbers, and was adopted in [[Extended Dyalog APL]] using the [[glyph]] <source lang=apl inline>⌾</source> as a monadic counterpart of [[Complex (function)|Complex]]. In other APL implementations that support complex numbers, [[Circular]] with the left argument of <source lang=apl inline>¯11</source> has the same functionality as Imaginary.
  
 
== Examples ==
 
== Examples ==

Revision as of 07:26, 4 June 2020

Imaginary () is a monadic scalar function which multiplies the argument by the imaginary unit 0J1, usually denoted or in traditional mathematics. This can be seen as a mapping from a real number to a pure imaginary number (a complex number with the real part of 0). It was added to J as j. together with initial support for complex numbers, and was adopted in Extended Dyalog APL using the glyph as a monadic counterpart of Complex. In other APL implementations that support complex numbers, Circular with the left argument of ¯11 has the same functionality as Imaginary.

Examples

Try it online!

       3 ¯4 6
0J3 0J¯4 0J6

Imaginary is equivalent to Complex with the default left argument of 0.

Try it online!

      0  3 ¯4 6
0J3 0J¯4 0J6

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, Atop, Over) ∙ Inner ProductPowerAtUnderRankDepthVariantStencilCut (J)
Quad names
Arrays Index originMigration levelAtomic vector
Functions Name classCase convertUnicode convert
Operators SearchReplace