Difference between revisions of "Or"
(Created page with "{{BuiltinOr∨}} 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...") 
(→Extended definition: Split the description for integers and nonintegers) 

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== Extended definition ==  == Extended definition ==  
−  Many APL implementations extend this function to nonBoolean arguments. In this case, this function behaves as '''[[wikipedia:Greatest common divisorGreatest 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  +  Many APL implementations extend this function to nonBoolean arguments. In this case, this function behaves as '''[[wikipedia:Greatest common divisorGreatest 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. 
<source lang=apl>  <source lang=apl>  
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9 1 1 3 1 1 3 1 1 9 1  9 1 1 3 1 1 3 1 1 9 1  
10 1 2 1 2 5 2 1 2 1 10  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 nonintegers, 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 integerGaussian integers]], when X and/or Y are [[complex]] numbers).  
+  
+  <source lang=apl>  
0.6∨13÷3  0.6∨13÷3  
0.06666666667  0.06666666667 
Revision as of 04:29, 1 June 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.
∨ 
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
Extended definition
Many APL implementations extend this function to nonBoolean arguments. In this case, this function behaves as 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.
∘.∨⍨ 0,⍳10
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
While the mathematical definition of GCD does not cover nonintegers, some implementations accept them as arguments. In this case, the return value of R←X∨Y
is chosen so that both X÷R
and Y÷R
are integers (or Gaussian integers, when X and/or Y are complex numbers).
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