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 ==
== Extension ==
Some dialects allow Union to work on [[major cell]]s:
Some dialects allow Union to work on [[major cell]]s:
[https://tio.run/##SyzI0U2pTMzJT9dNrShJzUtJTfn/P@JR2wQTBaNHvVvUHR2dnJyBQJ0rEihoDBN0cXF0VOd61DcVKBjxqGNV5P//AA Try it online!]<source lang=apl>
[https://tio.run/##SyzI0U2pTMzJT9dNrShJzUtJTfn/P@JR2wQTBaNHvVvUHR2dnJyBQJ0rEihoDBN0cXF0VOd61DcVKBjxqGNV5P//AA Try it online!]<syntaxhighlight lang=apl>
       X←4 2⍴'AABBCCCC'
       X←4 2⍴'AABBCCCC'
       Y←3 2⍴'AADDAA'
       Y←3 2⍴'AADDAA'
Line 27: Line 27:
CC
CC
DD
DD
</source>{{Works in|[[Extended Dyalog APL]]}}
</syntaxhighlight>{{Works in|[[Extended Dyalog APL]]}}
Others can easily define such a function:
Others can easily define such a function:
[https://tio.run/##SyzI0U2pTMzJT///P@JR2wQTBaNHvVvUHR2dnJyBQJ0rEihoDBN0cXF0VOcKzcvMzwMKVz/q3fWod9Wj3q2PevY/6l2h8ahzEVBI0wYsvhkoXsv1qG8qUGWEAliPQuT//wA Try it online!]<source lang=apl>
[https://tio.run/##SyzI0U2pTMzJT///P@JR2wQTBaNHvVvUHR2dnJyBQJ0rEihoDBN0cXF0VOcKzcvMzwMKVz/q3fWod9Wj3q2PevY/6l2h8ahzEVBI0wYsvhkoXsv1qG8qUGWEAliPQuT//wA Try it online!]<syntaxhighlight lang=apl>
       X←4 2⍴'AABBCCCC'
       X←4 2⍴'AABBCCCC'
       Y←3 2⍴'AADDAA'
       Y←3 2⍴'AADDAA'
Line 39: Line 39:
CC
CC
DD
DD
</source>{{Works in|[[Dyalog APL]]}}
</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 11:05, 11 September 2022

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


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