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.
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