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" <source 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>
<source lang=apl>
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│THIS│THAT│THE│OTHER│THAN│AND│
│THIS│THAT│THE│OTHER│THAN│AND│
└────┴────┴───┴─────┴────┴───┘
└────┴────┴───┴─────┴────┴───┘
</source>
</syntaxhighlight>


== Extension ==
== Extension ==
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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!]<source lang=apl>
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CC
CC
DD
DD
</source>{{Works in|[[Dyalog APL]]}}
</syntaxhighlight>{{Works in|[[Dyalog APL]]}}
== External Links ==
== External Links ==


Revision as of 10:35, 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" <source 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 arrays.

<source lang=apl> 

     '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│ └────┴────┴───┴─────┴────┴───┘ </syntaxhighlight>

Extension

Some dialects allow Union to work on major cells: Try it online!<source 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: Try it online!<source lang=apl> 

     X←4 2⍴'AABBCCCC'
     Y←3 2⍴'AADDAA'
     Intersection←{⍺⌿⍨(≢⍵)≥⍵⍳⍺}
     X Intersection Y

AA BB CC CC DD

</syntaxhighlight>

Works in: Dyalog APL

External Links

Documentation


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