On Feb 10, 11:01 am, William Stein <wst...@gmail.com> wrote: > On Thu, Feb 10, 2011 at 9:55 AM, William Stein <wst...@gmail.com> wrote: > > [... gcd stuff ...] > > It seems like nobody explained how the current gcd definition got > included. It's from a patch to rational.pyx from Alex Ghitza (who I > cc'd) that did this: > > - d = self.denom()*other.denom() > - self_d = self.numer()*other.denom() > - other_d = other.numer()*self.denom() > - return self_d.gcd(other_d) / d > + if self == 0 and other == 0: > + return Rational(0) > + else: > + return Rational(1) > > This was from trac 3214 "uniformise the behaviour of gcd for rational > numbers": > > http://trac.sagemath.org/sage_trac/ticket/3214 > > which was reported by Andrey Novoseltsev. > > So if Andrey or Alex cared so much, they may want to pipe up. > > This thread is at least: > > http://groups.google.com/group/sage-devel/browse_thread/thread/cd0558... > > William
Well, I used to use gcd for obtaining the primitive integral vector with a specified rational direction. My concern on Trac 3214 was that gcd(a1, ..., ak) depended on the order of arguments and I wanted it to be fixed. The eventual solution was to agree that gcd as the "greatest common divisor" does not really make much sense for fields, but instead of raising an exception it can just return 1. This meant that I cannot use it for my original purpose (not a big deal - it is easy to do more directly), but I think that it was quite a sensible decision: 1) I don't recall seeing gcd of rational numbers in any book or paper 2) there is clearly no natural extension of this notion from ZZ to QQ 3) the name itself indeed is very strange applied to fields. So I personally think that any kind of gcd/lcm combinations of numerators/denominators of rational numbers should have some other more appropriate names, since making up some conventions for gcd is potentially dangerous and may make code using it harder to understand if a reader thinks of gcd differently than the original author... Thank you, Andrey -- 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
