GCD in Fractions
Terry Reedy
tjreedy at udel.edu
Wed Sep 24 19:42:04 CEST 2014
On 9/24/2014 7:44 AM, Steven D'Aprano wrote:
> blindanagram wrote:
>
>> Seccondly (as others here have pointed out), the mathematical properties
>> of the greatest common divisor are well defined for both positive and
>> negative integers.
>
> You keep saying that, but it simply is not true. Different people use
> different definitions. Some refuse to allow negative arguments at all. Some
> insist that the GCD must be positive. Others allow it to be negative.
[convincing evidence of the above snipped]
The negative of the greatest common divisor is the least common divisor
(when the range includes negative integers). If a 'gcd' is allowed to
be negative, one must re-interpret 'gcd' as abbreviating
'greatest-magnitude common divisor'. It then might be better called 'gmcd'.
--
Terry Jan Reedy
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