gladman added the comment: On 24/09/2014 19:01, Mark Dickinson wrote: > > Mark Dickinson added the comment: > >> The negative of the greatest common divisor is the least common divisor in >> an integer range. > > That depends on your choice of definitions: it's perfectly reasonable to see > it as another greatest common divisor, if you interpret "greatest" as being > with respect to the divisibility lattice, not the total ordering of Z. > That's in some sense the correct interpretation, because it's the one that > generalises to other interesting rings: for example, the Gaussian integers > have a well-defined and useful notion of greatest common divisor, but aren't > ordered, and the ring Z[sqrt 3] similarly has well-defined greatest common > divisors (defined up to multiplication by a unit, as usual) *and* a total > ordering, but "greatest" *can't* be interpreted in the ordering sense in that > case (because there are infinitely many units). > > Many textbooks will talk about "a greatest common divisor" rather than "the > greatest common divisor". In that sense, -3 *is* a greatest common divisor > of 6 and -15.
Then the Python documentation should say 'a greatest ...', not 'the greatest ...' since those who deny that the integer gcd is non-negative can hardly deny that a positive alternative value exists :-) ---------- _______________________________________ Python tracker <rep...@bugs.python.org> <http://bugs.python.org/issue22477> _______________________________________ _______________________________________________ Python-bugs-list mailing list Unsubscribe: https://mail.python.org/mailman/options/python-bugs-list/archive%40mail-archive.com
