Union: Difference between revisions

 `∪`

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'
X∩Y
```

AA BB CC CC DD

</syntaxhighlight>

Others can easily define such a function: Try it online!<source lang=apl>

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

AA BB CC CC DD

</syntaxhighlight>

Works in: Dyalog APL