My personal feeling is that the current definition wrt negative integers is consistent and useful, so I think it is fine.
But, I'll be the first to admit that I am not expert in the field, so please take my opinion with a considerable grain of salt. On 3/31/2011 9:28, Brian Schott wrote: > Consider also that 2 negatives give a positive, too. > > And the following result is interesting, though likely irrelevant. > > 2r3 *. 3r4 > 6 > > > On Thu, Mar 31, 2011 at 9:19 AM, David Mitchell<[email protected]> wrote: >> AS I see it, LCM is defined in terms of GCD: >> >> "The least common multiple is the product divided by the GCD." >> >> One definition I found for GCD is this: >> >> In mathematics, the greatest common divisor (gcd), also known as the greatest >> common denominator, greatest common factor (gcf), or highest common factor >> (hcf), of two or more non-zero integers, is the largest positive integer that >> divides the numbers without a remainder. >> >> If GCD is always positive, given the definition of LCM, it looks like LCM >> will >> always be negative for augments with opposite signs. >> >> On 3/31/2011 8:58, Raul Miller wrote: >>> When I look up "least common multiple", I get definitions for its >>> result like "the smallest positive integer which is a multiple of both >>> numbers". >>> >>> Of course, that is bogus when one of the numbers is zero, and I am >>> still looking for a good definition. >>> >>> But when one of the arguments to *. is negative, and the other is >>> positive, I get a negative result instead of a positive result... I >>> think that this comes from using a definition of *%+. but is it >>> correct? >>> >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm >> > > > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
