On Friday, February 11, 2011, D. S. McNeil <dsm...@gmail.com> wrote: > Well, someone asked for more posts.. not sure this is what he had in mind. > ;-) >
That was me. I think this has been a great discussion. > Forgive my being a bear of little brain, but I've yet to grasp why > defining the default gcd rational function to be equal to 1 or (from > Simon) the lcm equal to 1 would be a _useful_ thing to do, independent > of the existence of perspectives from which it's the right > generalization. Who is going to call such a function? Who uses the > current rational gcd behaviour? > > (.. I have a sneaking suspicion that the reason the rational lcm > behaviour doesn't currently match the rational gcd behaviour is > because these functions aren't getting a lot of exercise, not even by > people strongly in the gcd(2/1,4)=1 camp.) > > > The Pari/Mma/(Sage lcm+Maxima gcd) behaviour has pretty much > everything I want. Agrees with integer values when denominator is 1, > and so obeys least-surprise principles; is informative; preserves many > nice properties of positive integer gcd/lcm; is used in many other > places. The current Sage rational gcd behaviour surprised the heck > out of me and did so silently; returns 1 for all arguments and so is > minimally informative; doesn't preserve said nice relationships; and > doesn't match the behaviours of any of Pari, Mma, Maple, Maxima, or > Magma -- it doesn't even match Sage for lcm. > > If the above doesn't speak to you in favour of the former I don't know > what else to say; we clearly have very different perspectives on > design! > > If we do wind up defining gcd and/or lcm to be l, could we at least > define new short-named functions, say rgcd and rlcm, which do what > (IMHO) they should? Then I can simply explain to people "Oh, in Sage > we use 'rgcd' and 'rlcm' for gcd and lcm" and forget I brought this up > in the first place. :^) > I vote for changing the defn of sage rational gcd to match the "Pari/Mma/(Sage lcm+Maxima gcd) " convention. Since +1 isn't having the desired effect, I vote with my BDFL powers instead. Somebody post a patch. - william > > Doug > > -- > Department of Earth Sciences > University of Hong Kong > > -- > 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 > -- William Stein Professor of Mathematics University of Washington http://wstein.org -- 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
