|Subject:||Re:[Axiom-developer] Re: [sage-devel] Re: sage thoughts|
|Date:||Sat, 12 Feb 2011 20:33:26 -0600|
|User-agent:||Mozilla/5.0 (X11; U; Linux i686 (x86_64); en-US; rv:220.127.116.11) Gecko/20101207 Thunderbird/3.1.7|
I haven't been paying close attention but I think the following might work:
define the gcd() implicitly: i.e. minimize over [m,n integer,G>0]( m(a/b)+n(c/d))=G
This seems to make sense in Euclidean domains.
This leads to
let's see how this works
gcd(1/4,1/6) would yield 2/24=1/12
gcd(3/12,9/54) would yield gcd(3*54,12*9)=gcd(3*9*6,3*4*9)=3*9*2
So it seems consistent.
Sorry if this is off-topic or I have overlooked something obvious. Of course the actual reasonableness and verification needs proof.
I think I have developed a formalism that makes sense over Principal Ideal Rings, extended to include inverses. Bur the ideas are not mathematically well defined.
On 02/11/2011 03:55 AM, daly wrote:
On Fri, 2011-02-11 at 01:49 -0800, Simon King wrote:
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