Difference between revisions of "Imaginary"

From APL Wiki
Jump to navigation Jump to search
 
Line 15: Line 15:
 
</source>{{Works in|[[Extended Dyalog APL]]}}
 
</source>{{Works in|[[Extended Dyalog APL]]}}
  
 +
== See also ==
 +
* [[Negate]]
 +
* [[Reciprocal]]
 +
== External links ==
 
=== Documentation ===
 
=== Documentation ===
  
 
* J [https://www.jsoftware.com/help/dictionary/djdot.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/jdot NuVoc]
 
* J [https://www.jsoftware.com/help/dictionary/djdot.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/jdot NuVoc]
 
{{APL built-ins}}[[Category:Primitive functions]][[Category:Scalar monadic functions]]
 
{{APL built-ins}}[[Category:Primitive functions]][[Category:Scalar monadic functions]]

Latest revision as of 07:09, 9 July 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

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