Intersection: 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 Intersection is usually implemented as "left argument [[replicate|filtered]] by its [[membership|existence]] in the right argument" <source lang=apl inline>(X∊Y)/X</source>, which preserves the order and multiplicity in the left argument. 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 Intersection is usually implemented as "left argument [[replicate|filtered]] by its [[membership|existence]] in the right argument" <syntaxhighlight lang=apl inline>(X∊Y)/X</syntaxhighlight>, which preserves the order and multiplicity in the left argument. Both arguments can be [[nested array|nested arrays]].


<source lang=apl>
<syntaxhighlight lang=apl>
       'ABRA'∩'CAR'
       'ABRA'∩'CAR'
ARA
ARA
Line 17: Line 17:
│AND│
│AND│
└───┘
└───┘
</source>
</syntaxhighlight>


== Extension ==
Some dialects allow Intersection to work on [[major cell]]s:
[https://tio.run/##SyzI0U2pTMzJT9dNrShJzUtJTfn/P@JR2wQTBaNHvVvUHR2dnJyBQJ0rEihojBB0dFTnetQ3FSgY8ahjZeT//wA Try it online!]<syntaxhighlight lang=apl>
      X←4 2⍴'AABBCCCC'
      Y←3 2⍴'AABBAA'
      X∩Y
AA
BB
</syntaxhighlight>{{Works in|[[Extended Dyalog APL]]}}
Others can easily define such a function:
[https://tio.run/##SyzI0U2pTMzJT///P@JR2wQTBaNHvVvUHR2dnJyBQJ0rEihojBB0dFTn8swrSS0qTk0uyczPA8pWP@rd9ahn/6PeFRqPOhc96t2q@ahzKZB61LsZKFPL9ahvKlBVhAKyNoXI//8B Try it online!]<syntaxhighlight lang=apl>
      X←4 2⍴'AABBCCCC'
      Y←3 2⍴'AABBAA'
      Intersection←{⍺⌿⍨(≢⍵)≥⍵⍳⍺}
      X Intersection Y
AA
BB
</syntaxhighlight>{{Works in|[[Dyalog APL]]}}
== External Links ==
== External Links ==


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


* [http://help.dyalog.com/latest/#Language/Primitive%20Functions/Intersection.htm Dyalog]
* [https://help.dyalog.com/latest/#Language/Primitive%20Functions/Intersection.htm Dyalog]
* [http://microapl.com/apl_help/ch_020_020_394.htm APLX]
* [http://microapl.com/apl_help/ch_020_020_394.htm APLX]


{{APL built-ins}}[[Category:Primitive functions]][[Category:Set functions]]
{{APL built-ins}}[[Category:Primitive functions]][[Category:Set functions]]

Latest revision as of 22:14, 10 September 2022

∩

Intersection (∩) is a dyadic set function which computes the set intersection 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 Intersection is usually implemented as "left argument filtered by its existence in the right argument" (X∊Y)/X, which preserves the order and multiplicity in the left argument. Both arguments can be nested arrays. 

      'ABRA'∩'CAR'
ARA
       A←'THIS' 'AND' 'THAT'                                                  
       A∩'T'
                              ⍝ (No match for the single character T)
       A∩'AND'
                              ⍝ (No match for any of the three characters A N D)
       A∩⊂'AND'
┌───┐
│AND│
└───┘

Extension

Some dialects allow Intersection to work on major cells:

Try it online!

      X←4 2⍴'AABBCCCC'
      Y←3 2⍴'AABBAA'
      X∩Y
AA
BB
Works in: Extended Dyalog APL

Others can easily define such a function:

Try it online!

      X←4 2⍴'AABBCCCC'
      Y←3 2⍴'AABBAA'
      Intersection←{⍺⌿⍨(≢⍵)≥⍵⍳⍺}
      X Intersection Y
AA
BB
Works in: Dyalog APL

External Links

Documentation


APL built-ins [edit]
Primitives (Timeline) Functions
Scalar
Monadic Conjugate ∙ Negate ∙ Signum ∙ Reciprocal ∙ Magnitude ∙ Exponential ∙ Natural Logarithm ∙ Floor ∙ Ceiling ∙ Factorial ∙ Not ∙ Pi Times ∙ Roll ∙ Type ∙ Imaginary ∙ Square Root
Dyadic Add ∙ Subtract ∙ Times ∙ Divide ∙ Residue ∙ Power ∙ Logarithm ∙ Minimum ∙ Maximum ∙ Binomial ∙ Comparison functions ∙ Boolean functions (And, Or, Nand, Nor) ∙ GCD ∙ LCM ∙ Circular ∙ Complex ∙ Root
Non-Scalar
Structural Shape ∙ Reshape ∙ Tally ∙ Depth ∙ Ravel ∙ Enlist ∙ Table ∙ Catenate ∙ Reverse ∙ Rotate ∙ Transpose ∙ Raze ∙ Mix ∙ Split ∙ Enclose ∙ Nest ∙ Cut (K) ∙ Pair ∙ Link ∙ Partitioned Enclose ∙ Partition
Selection First ∙ Pick ∙ Take ∙ Drop ∙ Unique ∙ Identity ∙ Stop ∙ Select ∙ Replicate ∙ Expand ∙ Set functions (Intersection ∙ Union ∙ Without) ∙ Bracket indexing ∙ Index ∙ Cartesian Product ∙ Sort
Selector Index generator ∙ Grade ∙ Index Of ∙ Interval Index ∙ Indices ∙ Deal ∙ Prefix and suffix vectors
Computational Match ∙ Not Match ∙ Membership ∙ Find ∙ Nub Sieve ∙ Encode ∙ Decode ∙ Matrix Inverse ∙ Matrix Divide ∙ Format ∙ Execute ∙ Materialise ∙ Range
Operators Monadic Each ∙ Commute ∙ Constant ∙ Replicate ∙ Expand ∙ Reduce ∙ Windowed Reduce ∙ Scan ∙ Outer Product ∙ Key ∙ I-Beam ∙ Spawn ∙ Function axis
Dyadic Bind ∙ Compositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner Product ∙ Determinant ∙ Power ∙ At ∙ Under ∙ Rank ∙ Depth ∙ Variant ∙ Stencil ∙ Cut ∙ Direct definition (operator)
Quad names Index origin ∙ Comparison tolerance ∙ Migration level ∙ Atomic vector
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