Membership

Membership (∊), also called Member In, Member Of, or Element of, is a dyadic primitive function which tests if each of the elements of the left argument appears as an element of the right argument. Membership derives from the traditional mathematical notation $\in$ (Element of) and therefore uses that glyph (lunate epsilon).

Examples

Both arguments can be arrays of any shape. Each element of the left argument is tested against elements of the right argument, and the result is a boolean array having the same shape as the left argument.

      'THIS NOUN'∊'THAT WORD'
1 1 0 0 1 0 1 0 0
      3 6 9∊3 3⍴⍳9
1 1 1
      (3 3⍴⍳9)∊3 6 9
0 0 1
0 0 1
0 0 1

For nested arrays, Membership tests for exact match between the elements.

      'CAT' 'DOG' 'MOUSE' ∊ 'CAT' 'FOX' 'DOG' 'LLAMA'
1 1 0

Leading axis model

The behavior of Membership was changed to follow leading axis model in some implementations such as J (spelled e.). In this case, if the right argument is a higher-rank array, the cells of the left argument with appropriate rank are compared against the major cells of the right argument.

      ]mat=.>'able';'acre';'idle'
able
acre
idle
      'able' e. mat
1
      (<'able') e. mat
0
      'ab' e. mat
0
      (3 3 4$'able') e. mat  NB. the resulting shape is trailing axes (corresponding to the major cells of mat) removed
1 1 1
1 1 1
1 1 1

In other dialects, a leading axis membership function can be defined as:

      Membership←{(≢⍵)≥⍵⍳⍺}
      ⎕←mat←3 4⍴'ableacreidle'
able
acre
idle
      'able' Membership mat
1

Works in: Dyalog APL, NARS2000, dzaima/APL, Extended Dyalog APL, GNU 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 ∙ Round
		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 ∙ Identity (Null, Ident)
Operators	Dyadic	Bind ∙ Compositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner Product ∙ Determinant ∙ Power ∙ At ∙ Under ∙ Rank ∙ Depth ∙ Variant ∙ Stencil ∙ Cut ∙ Direct definition (operator) ∙ Identity (Lev, Dex)
Quad names	Index origin ∙ Comparison tolerance ∙ Migration level ∙ Atomic vector

Membership

Contents

Examples

Leading axis model

See also

External links

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Membership

Examples

Leading axis model

See also

External links

Documentation

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