Intersection

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

Dyalog
APLX

APL built-ins [edit]
Primitive 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 ∙ Select ∙ Replicate ∙ Expand ∙ Set functions (Intersection ∙ Union ∙ Without) ∙ Bracket indexing ∙ Index
		Selector	Index generator ∙ Grade ∙ Index Of ∙ Interval Index ∙ Indices ∙ Deal
		Computational	Match ∙ Not Match ∙ Membership ∙ Find ∙ Nub Sieve ∙ Encode ∙ Decode ∙ Matrix Inverse ∙ Matrix Divide ∙ Format ∙ Execute ∙ Materialise ∙ Range
Primitive operators	Monadic	Each ∙ Commute ∙ Constant ∙ Replicate ∙ Expand ∙ Reduce ∙ Windowed Reduce ∙ Scan ∙ Outer Product ∙ Key ∙ I-Beam ∙ Spawn ∙ Function axis
Primitive operators	Dyadic	Bind ∙ Compositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner Product ∙ Power ∙ At ∙ Under ∙ Rank ∙ Depth ∙ Variant ∙ Stencil ∙ Cut (J)
Quad names
	Arrays	Index origin ∙ Migration level ∙ Atomic vector
	Functions	Name class ∙ Case convert ∙ Unicode convert
	Operators	Search ∙ Replace

Intersection

Contents

Examples

Extension

External Links

Documentation

Navigation menu

Intersection

Examples

Extension

External Links

Documentation

Navigation menu

Search