Difference between revisions of "Without"

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m (Text replacement - "http://help.dyalog.com" to "https://help.dyalog.com")
 
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=== Documentation ===
 
=== Documentation ===
  
* [http://help.dyalog.com/latest/#Language/Primitive%20Functions/Excluding.htm#Excluding Dyalog]
+
* [https://help.dyalog.com/latest/#Language/Primitive%20Functions/Excluding.htm#Excluding Dyalog]
 
* [http://microapl.com/apl_help/ch_020_020_410.htm APLX]
 
* [http://microapl.com/apl_help/ch_020_020_410.htm APLX]
 
* J [https://www.jsoftware.com/help/dictionary/d121.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/minusdot#dyadic NuVoc]
 
* J [https://www.jsoftware.com/help/dictionary/d121.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/minusdot#dyadic NuVoc]
  
 
{{APL built-ins}}[[Category:Primitive functions]][[Category:Set functions]]
 
{{APL built-ins}}[[Category:Primitive functions]][[Category:Set functions]]

Latest revision as of 14:46, 14 July 2020

~

Without (~), Set Difference, Excluding, or Less, is a dyadic set function which computes the set difference of the two vector arguments. It shares the glyph ~ with the monadic function Not.

Examples

Both arguments of Without is usually restricted to vectors. Unlike sets in the mathematical sense, duplicate elements are allowed in both sides, and Without is usually implemented as "left argument filtered by the absence in the right argument" (~XY)/X. This preserves the order and multiplicity in the left argument. Both arguments can be nested arrays.

      'HELLO'~'GOODBYE'
HLL
      A'THIS' 'AND' 'THAT'
      A~'TH' 'AND'
┌────┬────┐
THISTHAT
└────┴────┘

Extension

Some dialects allow Without to work on major cells:

Try it online!

      X4 2'AABBCCCC'
      Y3 2'AABBAA'
      X~Y
CC
CC

Others can easily define such a function:

Try it online!

      X4 2'AABBCCCC'
      Y3 2'AABBAA'
      Without{⌿⍨~(⍳≢)}
      X Without Y
CC
CC
Works in: Dyalog APL

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 Case convertUnicode convert
Operators SearchReplace