On Sunday, August 12, 2018 at 1:01:28 PM UTC-7, Jeroen Demeyer wrote: > > On 2018-08-12 17:39, vdelecroix wrote: > > To construct the element x^-1 one has to use 1 // x because // > > stands for "internal division" in Sage > > What does "internal division" mean? I would define // as Euclidean > division (in some unspecified way since Euclidean division is not > unique). So I wonder how you would define a // b on the Laurent > polynomial ring in general (where b is not a power of x). > > I would define a // b on the Laurent polynomial ring simply as extending > the operation // of ordinary polynomials. That way, 1 // x should be 0. >
>From a practical point of view, as I pointed out a few months back in this thread, I am finding I much more often need to divide ring elements by a divisor than a euclidean division. When I need a euclidean division, I almost always need the remainder or both the "quotient" and the remainder. So euclidean division via "//" is almost useless to me. Therefore, I wouldn't mind using "//" as a partial division operation (give the quotient in the ring if it exists and an error otherwise). At least when it returns an answer, it's consistent with euclidean division. Extending it beyond that is actually a nuisance to me. -- 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.
