
From:  Raymond Rogers 
Subject:  Re:[Axiomdeveloper] Re: [sagedevel] Re: sage thoughts 
Date:  Sat, 12 Feb 2011 20:33:26 0600 
Useragent:  Mozilla/5.0 (X11; U; Linux i686 (x86_64); enUS; rv:1.9.2.13) 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 G=gcd(da,bc)/bd 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 3*9*2/(3*4*9*6)=1/12 So it seems consistent. Sorry if this is offtopic 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. Ray On 02/11/2011 03:55 AM, daly wrote: On Fri, 20110211 at 01:49 0800, Simon King wrote: 
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