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→Extended definition: Split the description for integers and non-integers
(Created page with "{{Built-in|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...") |
(→Extended definition: Split the description for integers and non-integers) |
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== Extended definition == | == Extended definition == | ||
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 | 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. | ||
<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 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 | 0.6∨13÷3 | ||
0.06666666667 | 0.06666666667 | ||