----- Original Message ----- From: "Martin v. Loewis" <email@example.com> To: "François Pinard" <firstname.lastname@example.org> Cc: "Mark J. Nenadov" <email@example.com>;
firstname.lastname@example.org Sent: Monday, May 27, 2002 2:21 AM Subject: Re: [Python-Dev] Re: Stability and change
email@example.com (François Pinard) writes: > > I also use 2.0 as the lowest common denominator. > > Linguistic problem :-). Should we say "greatest" instead of "lowest"? > Granted that the greatest common denominator is not "greatest" in any
> way, but it is lower or equal than any of the things we consider. The
> "lowest" common denominator might be very close to nothing, might it
For any two natural numbers, the lowest common denominator is 1. Finding the greatest (largest?) common denominator is indeed what involves an algorithm.
This terminology came from fractions. The canonical form of a fraction uses the lowest possible number as the denominator. When performing additive operations on fractions, the easiest way to proceed is to convert them to a form with the same number as a denominator. The usual choice is the lowest common denominator, which is the smallest number that can be used as the denominator in both fractions. This is the LCM (least common multiple) of the two denominators.
2/3 + 3/8 = 16/24 + 9/24 [24 being the LCD] = 25/24 = 1 1/24
It doesn't therefore (IMO) make much sense to talk about the lowest common denominator of any two natural numbers. The LCM, yes. The LCD, no.
It makes even less sense to talk about the lowest common denominator of Python implementations, except in the metaphorical sense Mark (I believe) intended.
Steve Holden http://www.holdenweb.com/