[Axiom-developer] Re: [sage-devel] Re: sage thoughts

[daly]

On Fri, 2011-02-11 at 01:49 -0800, Simon King wrote:
> Hi,
> 
> On 11 Feb., 09:56, Simon King <address@hidden> wrote:
> > Well, I had the impression that a couple of people are in favour of
> > the following:
> >  gcd(a/b,c/d) := gcd(a,c)/lcm(b,d)
> >  lcm(a/b,c/d) := lcm(a,c)/gcd(b,d)
> 
> It just occurs to me that I am incredibly stupid.
> 
> The definition above wouldn't work at all, it isn't even well-defined.
> Just replace gcd(1/4,1/6) by gcd(3/12,9/54). You obtain gcd(1,1)/
> lcm(4,6) = 1/12,  but gcd(3,9)/lcm(12,54) = 1/36.
> 
> Does anyone have a better idea? Would it be a correct definition if
> one insisted on reduced fractions?
> 
> Cheers,
> Simon
> 
That's why I was asking for an algorithm for gcd and lcm
in the subdomain. I'm not sure what answer is expected.
The unit (1) is correct but not by your definition, and
apparently not helpful for the original poster.

Tim Daly