Hi Doug! On 10 Feb., 09:40, "D. S. McNeil" <dsm...@gmail.com> wrote: > @Simon King: as you note, there are multiple ways to extend the > concept of gcds and lcms to the rationals. In such a situation, it > would seem that two minimal things you would like would be (1) to > reduce to the integer case for integer values, and (2) to maintain > some nice properties so that the names "gcd" and "lcm" still fit. > Given some definition satisfying (1), coercing down to integers from > rationals isn't much of a problem, ...
There is no "coercing down to integers from rationals". One important property of a coercion map is that it is a map, in contrast to a partial map. Actually, it even is a morphism. So, a coercion from QQ to ZZ would presumably be a morphism from QQ to ZZ in the category of unital rings - which doesn't exist. When I wrote "lcm(2/1,4) should not raise an error but use coercion", I meant of course that the integer 4 should be coerced into the common parent of 2/1 and 4, which is the rational field. > Choosing any definition > which doesn't reduce to the integer one, as is currently done, seems > problematic to me as a design decision, given that it's far more > likely to be used that way in error than it is that someone decided to > obfuscate "1" by writing it as gcd(some rational, some integer). No, I think you are mistaken. If you work with a,b rational or, worse, real numbers, then it is very highly unlikely that a and b *are* integers if they happen to seem like integers. Just think of rounding errors. This is another reason why "coercing down to the integers" won't make sense: It is highly unlikely that 1.0 really is the integer number 1. So, I think it is by far better to have a consistent notion than to have to *guess* whether a user really means the integer 2 if s/he write 4/2 (which in the first place is a rational, not an integer). Bugs that are result of guesswork are the most ugly, IMHO. Cheers, Simon -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
