On Sat, Dec 10, 2011 at 11:52 PM, Keshav Kini <keshav.k...@gmail.com> wrote: > Correct me if I'm wrong, but divisibility is only a partial order (and thus > gcds are only unique) modulo associates. Everything but 0 is a unit in Z/7Z, > an integral domain, so any of 1, 2, 3, 4, 5, or 6 would be an acceptable > value for the gcd of 5 and 7(=0), no? Or is the "common parent" something > other than Z/7Z?
Yes, you would be right if the parent were Z/7Z. The natural choice for the parent should *definitely* be Z/7Z, since: sage: Sequence([Mod(5,7), 7]).universe() Ring of integers modulo 7 Any of the choices you mentioned above would be fine, but 5 is the best answer, just like this is best: sage: gcd(6/1, 9/1) 3 sage: parent(gcd(6/1, 9/1)) Rational Field Now as you noticed, we have sage: gcd(Mod(5,7), 7) 5 sage: parent(gcd(Mod(5,7), 7)) Integer Ring which... sucks! I consider this a bug. We should definitely have that the gcd is in parent(Mod(5,7)). William > I do see > > sage: gcd(Integers(7)(5), 7) > 5 > sage: gcd(Integers(7)(5), 7).parent() is ZZ > True > > which makes no sense. > > -Keshav > > ---- > Join us in #sagemath on irc.freenode.net ! > > -- > 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
