Difference between revisions of "And"
(→Extended definition: Split the description for integers and nonintegers) 
(→External links: APLX) 

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* [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 builtins}}[[Category:Primitive functions]][[Category:Scalar dyadic functions]]  {{APL builtins}}[[Category:Primitive functions]][[Category:Scalar dyadic functions]] 
Revision as of 15:06, 1 June 2020
∧

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
When combined with Reduce, And can be used to test if every value in a Boolean vector is true.
∧/ 1 1 1 1 1
1
∧/ 1 0 0 1 1
0
Extended definition
Many APL implementations extend this function to nonBoolean 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.
∘.∧⍨ 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
While the mathematical definition of LCM 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 R÷X
and R÷Y
are integers (or Gaussian integers, when X and/or Y are complex numbers).
0.9∧25÷6
112.5
112.5÷0.9(25÷6)
125 27
2J2∧3J1
6J2
6J2÷2J2 3J1
2J¯1 2