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Revision as of 15:09, 1 June 2020

885 bytes removed ,  15:09, 1 June 2020
Move LCM to its own page; see Talk:Or
(Created page with "{{Built-in|And|∧}} is a dyadic 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 wi...")
 
(Move LCM to its own page; see Talk:Or)
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{{Built-in|And|∧}} is a [[dyadic]] [[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 [[wikipedia:logical conjunction|logical conjunction]] in Boolean logic.
{{Built-in|And|∧}} is a [[dyadic]] [[scalar function|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 [[wikipedia:logical conjunction|logical conjunction]] in Boolean logic. In many APLs, And is a special case of the [[LCM]] function.


{|class=wikitable
{|class=wikitable
!<source lang=apl inline>=</source>!!<source lang=apl inline>0</source>!!<source lang=apl inline>1</source>
!<source lang=apl inline>∧</source>!!<source lang=apl inline>0</source>!!<source lang=apl inline>1</source>
|-
|-
!<source lang=apl inline>0</source>
!<source lang=apl inline>0</source>
Line 20: Line 20:
</source>
</source>


== Extended definition ==
When combined with [[Reduce]], And can be used to test if every value in a Boolean vector is true.
 
Many APL implementations extend this function to non-Boolean arguments. In this case, this function behaves as '''[[wikipedia:Least common multiple|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 [[wikipedia:Gaussian integer|Gaussian integers]], when given [[complex]] numbers).


<source lang=apl>
<source lang=apl>
       ∘.∧⍨ 0,⍳10
       ∧/ 1 1 1 1 1
0  0  0  0  0  0  0  0  0  0  0
1
0  1 2  3  4  5  6  7  8  9 10
      ∧/ 1 0 0 1 1
0 2  2  6  4 10  6 14  8 18 10
0
0 3  6  3 12 15  6 21 24  9 30
</source>
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
 
      0.9∧25÷6
112.5
      112.5÷0.9(25÷6)
125 27
      2J2∧3J1
6J2
      6J2÷2J2 3J1
2J¯1 2
</source>{{Works in|[[Dyalog APL]]}}


== External links ==
== External links ==
Line 53: Line 34:


* [http://help.dyalog.com/17.1/#Language/Primitive%20Functions/And%20Lowest%20Common%20Multiple.htm Dyalog]
* [http://help.dyalog.com/17.1/#Language/Primitive%20Functions/And%20Lowest%20Common%20Multiple.htm Dyalog]
* [http://microapl.com/apl_help/ch_020_020_430.htm APLX]
* J [https://www.jsoftware.com/help/dictionary/d111.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/stardot#dyadic NuVoc]
* J [https://www.jsoftware.com/help/dictionary/d111.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/stardot#dyadic NuVoc]
{{APL built-ins}}[[Category:Primitive functions]][[Category:Scalar dyadic functions]]
{{APL built-ins}}[[Category:Primitive functions]][[Category:Scalar dyadic functions]]
Retrieved from ‘https://aplwiki.com/wiki/Special:MobileDiff/4601...4630’

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