And

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And () is a dyadic scalar boolean function which tests if both arguments are true: it returns 1 if both are 1 and 0 if one or both are 0. It represents the logical conjunction in Boolean logic.

0 1
0 0 0
1 0 1

Examples

The following shows all possible combinations of inputs as a Boolean function.

      0 0 1 1  0 1 0 1
0 0 0 1

Extended definition

Many APL implementations extend this function to non-Boolean arguments. In this case, this function behaves as Least Common Multiple or LCM. For positive integer arguments, it is defined as the smallest positive number which is divisible by both numbers. If one of the arguments is zero, the LCM function returns zero. While the mathematical definition of LCM does not cover non-integers, some implementations accept them as arguments, returning a value which, when divided by both arguments, gives integers (or Gaussian integers, when given complex numbers).

      ∘. 0,⍳10
0  0  0  0  0  0  0  0  0  0  0
0  1  2  3  4  5  6  7  8  9 10
0  2  2  6  4 10  6 14  8 18 10
0  3  6  3 12 15  6 21 24  9 30
0  4  4 12  4 20 12 28  8 36 20
0  5 10 15 20  5 30 35 40 45 10
0  6  6  6 12 30  6 42 24 18 30
0  7 14 21 28 35 42  7 56 63 70
0  8  8 24  8 40 24 56  8 72 40
0  9 18  9 36 45 18 63 72  9 90
0 10 10 30 20 10 30 70 40 90 10

      0.925÷6
112.5
      112.5÷0.9(25÷6)
125 27
      2J23J1
6J2
      6J2÷2J2 3J1
2J¯1 2
Works in: Dyalog APL

External links

Documentation

APL built-ins [edit]
Primitive functions
Scalar
Monadic ConjugateNegateSignumReciprocalMagnitudeExponentialNatural LogarithmFloorCeilingFactorialNotPi TimesRollTypeImaginarySquare Root
Dyadic AddSubtractTimesDivideResiduePowerLogarithmMinimumMaximumBinomialComparison functionsBoolean functions (And, Or, Nand, Nor) ∙ GCDLCMCircularComplexRoot
Non-Scalar
Structural ShapeReshapeTallyDepthRavelEnlistTableCatenateReverseRotateTransposeRazeMixSplitEncloseNestCut (K)PairLinkPartitioned EnclosePartition
Selection FirstPickTakeDropUniqueIdentitySelectReplicateExpandSet functions (IntersectionUnionWithout) ∙ Bracket indexingIndex
Selector Index generatorGradeIndex OfInterval IndexIndicesDeal
Computational MatchNot MatchMembershipFindNub SieveEncodeDecodeMatrix InverseMatrix DivideFormatExecuteMaterialise
Primitive operators Monadic EachCommuteConstantReplicateExpandReduceWindowed ReduceScanOuter ProductKeyI-beamSpawnFunction axis
Dyadic BindCompositions (Compose, Reverse Compose, Beside, Atop, Over) ∙ Inner ProductPowerAtUnderRankDepthVariantStencil
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