Union: Difference between revisions

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== Examples ==
== Examples ==


Both arguments of Intersection is usually restricted to [[vector|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" <source lang=apl inline>X,(~Y∊X)/Y</source>. This preserves the order and multiplicity in both arguments, the left one taking precedence. Both arguments can be [[nested array|nested arrays]].
Both arguments of Intersection is usually restricted to [[vector|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" <syntaxhighlight lang=apl inline>X,(~Y∊X)/Y</syntaxhighlight>. This preserves the order and multiplicity in both arguments, the left one taking precedence. Both arguments can be [[nested array|nested arrays]].


<source lang=apl>
<syntaxhighlight lang=apl>
       'WASH' ∪ 'SHOUT'
       'WASH' ∪ 'SHOUT'
WASHOUT
WASHOUT
Line 14: Line 14:
│THIS│THAT│THE│OTHER│THAN│AND│
│THIS│THAT│THE│OTHER│THAN│AND│
└────┴────┴───┴─────┴────┴───┘
└────┴────┴───┴─────┴────┴───┘
</source>
</syntaxhighlight>


== Extension ==
Some dialects allow Union to work on [[major cell]]s:
[https://tio.run/##SyzI0U2pTMzJT9dNrShJzUtJTfn/P@JR2wQTBaNHvVvUHR2dnJyBQJ0rEihoDBN0cXF0VOd61DcVKBjxqGNV5P//AA Try it online!]<syntaxhighlight lang=apl>
      X←4 2⍴'AABBCCCC'
      Y←3 2⍴'AADDAA'
      X∩Y
AA
BB
CC
CC
DD
</syntaxhighlight>{{Works in|[[Extended Dyalog APL]]}}
Others can easily define such a function:
[https://tio.run/##SyzI0U2pTMzJT///P@JR2wQTBaNHvVvUHR2dnJyBQJ0rEihoDBN0cXF0VOcKzcvMzwMKVz/q3fWod9Wj3q2PevY/6l2h8ahzEVBI0wYsvhkoXsv1qG8qUGWEAliPQuT//wA Try it online!]<syntaxhighlight lang=apl>
      X←4 2⍴'AABBCCCC'
      Y←3 2⍴'AADDAA'
      Union←{⍺⍪⍵⌿⍨(≢⍺)<⍺⍳⍵}
      X Union Y
AA
BB
CC
CC
DD
</syntaxhighlight>{{Works in|[[Dyalog APL]]}}
== External Links ==
== External Links ==


=== Documentation ===
=== Documentation ===


* [http://help.dyalog.com/latest/#Language/Primitive%20Functions/Union.htm Dyalog]
* [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 17:25, 6 January 2024

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,(~Y∊X)/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 3∪5 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'
┌────┬────┬───┬─────┬────┬───┐
│THIS│THAT│THE│OTHER│THAN│AND│
└────┴────┴───┴─────┴────┴───┘

Extension

Some dialects allow Union to work on major cells:

Try it online!

      X←4 2⍴'AABBCCCC'
      Y←3 2⍴'AADDAA'
      X∩Y
AA
BB
CC
CC
DD

Others can easily define such a function:

Try it online!

      X←4 2⍴'AABBCCCC'
      Y←3 2⍴'AADDAA'
      Union←{⍺⍪⍵⌿⍨(≢⍺)<⍺⍳⍵}
      X Union Y
AA
BB
CC
CC
DD
Works in: Dyalog APL

External Links

Documentation


APL built-ins [edit]
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Scalar
Monadic ConjugateNegateSignumReciprocalMagnitudeExponentialNatural LogarithmFloorCeilingFactorialNotPi TimesRollTypeImaginarySquare Root
Dyadic AddSubtractTimesDivideResiduePowerLogarithmMinimumMaximumBinomialComparison functionsBoolean functions (And, Or, Nand, Nor) ∙ GCDLCMCircularComplexRoot
Non-Scalar
Structural ShapeReshapeTallyDepthRavelEnlistTableCatenateReverseRotateTransposeRazeMixSplitEncloseNestCut (K)PairLinkPartitioned EnclosePartition
Selection FirstPickTakeDropUniqueIdentityStopSelectReplicateExpandSet functions (IntersectionUnionWithout) ∙ Bracket indexingIndexCartesian ProductSort
Selector Index generatorGradeIndex OfInterval IndexIndicesDealPrefix and suffix vectors
Computational MatchNot MatchMembershipFindNub SieveEncodeDecodeMatrix InverseMatrix DivideFormatExecuteMaterialiseRange
Operators Monadic EachCommuteConstantReplicateExpandReduceWindowed ReduceScanOuter ProductKeyI-BeamSpawnFunction axis
Dyadic BindCompositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner ProductDeterminantPowerAtUnderRankDepthVariantStencilCutDirect definition (operator)
Quad names Index originComparison toleranceMigration levelAtomic vector