Difference between revisions of "Or"

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{{Built-in|Or|∨}} is a [[dyadic]] [[scalar function|scalar]] [[boolean function]] which tests if at least one of the two arguments is true: it returns 1 if at least one side is 1 and 0 if both are 0. It represents the [[wikipedia:logical disjunction|logical disjunction]] in Boolean logic.
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{{Built-in|Or|∨}} is a [[dyadic]] [[scalar function|scalar]] [[boolean function]] which tests if at least one of the two arguments is true: it returns 1 if at least one side is 1 and 0 if both are 0. It represents the [[wikipedia:logical disjunction|logical disjunction]] in Boolean logic. In many APLs, Or is a special case of the [[GCD]] function.
  
 
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</source>
 
</source>
  
== Extended definition ==
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== See also ==
 
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* [[Add]]
Many APL implementations extend this function to non-Boolean arguments. In this case, this function behaves as '''[[wikipedia:Greatest common divisor|Greatest Common Divisor]]''' or '''GCD'''. For positive integer arguments, it is defined as the largest positive number which divides both numbers. If one of the arguments is zero, the GCD function returns the other number.
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* [[Maximum]]
 
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* [[Union]]
<source lang=apl>
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* [[Nor]]
      ∘.∨⍨ 0,⍳10
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* [[And]]
0 1 2 3 4 5 6 7 8 9 10
 
1 1 1 1 1 1 1 1 1 1  1
 
2 1 2 1 2 1 2 1 2 1  2
 
3 1 1 3 1 1 3 1 1 3  1
 
4 1 2 1 4 1 2 1 4 1  2
 
5 1 1 1 1 5 1 1 1 1  5
 
6 1 2 3 2 1 6 1 2 3  2
 
7 1 1 1 1 1 1 7 1 1  1
 
8 1 2 1 4 1 2 1 8 1  2
 
9 1 1 3 1 1 3 1 1 9  1
 
10 1 2 1 2 5 2 1 2 1 10
 
</source>{{Works in|[[Dyalog APL]]}}
 
 
 
While the mathematical definition of GCD does not cover non-integers, some implementations accept them as arguments. In this case, the return value of <source lang=apl inline>R←X∨Y</source> is chosen so that both <source lang=apl inline>X÷R</source> and <source lang=apl inline>Y÷R</source> are integers (or [[wikipedia:Gaussian integer|Gaussian integers]], when X and/or Y are [[complex]] numbers).
 
 
 
<source lang=apl>
 
      0.6∨13÷3
 
0.06666666667
 
      0.6(13÷3)÷0.6∨13÷3
 
9 65
 
      2J2∨3J1
 
1J1
 
      2J2 3J1÷1J1
 
2 2J¯1
 
</source>{{Works in|[[Dyalog APL]]}}
 
  
 
== External links ==
 
== External links ==
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=== Documentation ===
 
=== Documentation ===
  
* [http://help.dyalog.com/17.1/#Language/Primitive%20Functions/Or%20Greatest%20Common%20Divisor.htm Dyalog]
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* [https://help.dyalog.com/17.1/#Language/Primitive%20Functions/Or%20Greatest%20Common%20Divisor.htm Dyalog]
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* [http://microapl.com/apl_help/ch_020_020_420.htm APLX]
 
* J [https://www.jsoftware.com/help/dictionary/d101.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/plusdot#dyadic NuVoc]
 
* J [https://www.jsoftware.com/help/dictionary/d101.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/plusdot#dyadic NuVoc]
 
{{APL built-ins}}[[Category:Primitive functions]][[Category:Scalar dyadic functions]]
 
{{APL built-ins}}[[Category:Primitive functions]][[Category:Scalar dyadic functions]]

Latest revision as of 14:48, 14 July 2020

Or () is a dyadic scalar boolean function which tests if at least one of the two arguments is true: it returns 1 if at least one side is 1 and 0 if both are 0. It represents the logical disjunction in Boolean logic. In many APLs, Or is a special case of the GCD function.

0 1
0 0 1
1 1 1

Examples

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

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

When combined with Reduce, Or can be used to test if some value in a Boolean vector is true.

      / 0 0 1 0 1
1
      / 0 0 0 0 0
0

See also

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 DivideFormatExecuteMaterialiseRange
Primitive operators Monadic EachCommuteConstantReplicateExpandReduceWindowed ReduceScanOuter ProductKeyI-beamSpawnFunction axis
Dyadic BindCompositions (Compose, Reverse Compose, Beside, Atop, Over) ∙ Inner ProductPowerAtUnderRankDepthVariantStencilCut (J)
Quad names
Arrays Index originMigration levelAtomic vector
Functions Case convertUnicode convert
Operators SearchReplace