Well, someone asked for more posts.. not sure this is what he had in mind. ;-)
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. :^) 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
