Presumably nobody has a problem with sage: R.<x> = QQ[] sage: (3*x^2+1) // (2*x) 3/2*x
and it would be rather strange if the binary operations on the scalars behave different in QQ vs degree-0-part(QQ[x]). Whereas it shouldn't come as too much of a surprise that division-related operations behave differently in ZZ and QQ. On Tuesday, January 19, 2016 at 9:09:28 PM UTC, Jeroen Demeyer wrote: > > On 2016-01-19 13:31, John Cremona wrote: > > This would only make sense if ZZ was the only ring of which QQ was the > > field of fractions. Similarly with rational function fields, in my > > opinion. > > Well, you are thinking too mathematical. Of course, defining a//b = a/b > makes any field into a Euclidean domain. However, this isn't very > useful. If the user really wanted to just divide rational numbers, then > he could just write a/b instead of a//b. > > > Defining // on QQ as extending // from ZZ is a lot more useful and > intuitive, even though it's not canonical from a mathematical point of > view. > > Jeroen. > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
