Difference between revisions of "Union"

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=== Documentation ===
 
=== Documentation ===
  
* [http://help.dyalog.com/latest/#Language/Primitive%20Functions/Union.htm Dyalog]
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* [https://help.dyalog.com/latest/#Language/Primitive%20Functions/Union.htm Dyalog]
 
* [http://microapl.com/apl_help/ch_020_020_393.htm APLX]
 
* [http://microapl.com/apl_help/ch_020_020_393.htm APLX]
  
 
{{APL built-ins}}[[Category:Primitive functions]][[Category:Set functions]]
 
{{APL built-ins}}[[Category:Primitive functions]][[Category:Set functions]]

Latest revision as of 14:36, 14 July 2020

Union () is a dyadic set function which computes the set union of the two vector arguments.

Examples

Both arguments of Intersection is usually restricted to vectors. Unlike sets in the mathematical sense, duplicate elements are allowed in both sides, and Union is usually implemented as "left argument unchanged, plus the elements of right argument not in the left argument" X,(~YX)/Y. This preserves the order and multiplicity in both arguments, the left one taking precedence. Both arguments can be nested arrays.

      'WASH'  'SHOUT'
WASHOUT
      1 2 3 1 2 3 1 2 35 4 3 2 5 4 3 2
1 2 3 1 2 3 1 2 3 5 4 5 4
      'THIS' 'THAT' 'THE' 'OTHER''OTHER' 'THAN' 'THIS' 'AND' 'THAT'
┌────┬────┬───┬─────┬────┬───┐
THISTHATTHEOTHERTHANAND
└────┴────┴───┴─────┴────┴───┘

Extension

Some dialects allow Union to work on major cells:

Try it online!

      X4 2'AABBCCCC'
      Y3 2'AADDAA'
      XY
AA
BB
CC
CC
DD

Others can easily define such a function:

Try it online!

      X4 2'AABBCCCC'
      Y3 2'AADDAA'
      Intersection{⌿⍨()}
      X Intersection Y
AA
BB
CC
CC
DD
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