On Sunday, June 10, 2018 at 12:12:46 AM UTC+10, vdelecroix wrote: > > On 09/06/2018 04:00, Travis Scrimshaw wrote: > > What Vincent has neglected to mention is the reasoning why I am > suggesting > > to keep the current behavior for Laurent polynomials. A casual user will > > almost certainly do > > > > 1 / x^k > > > > and then try to do a method on Laurent polynomials (say, iterate over > such > > element). The rational functions code does not have many of the methods > and > > features that Laurent polynomials have. > > > > Also, they (or at least I) would be quite surprised when x^-1 does not > > behave the same as 1/x as they are mathematically equivalent. Also, what > > about ~x, should that be the same as 1/x or x^-1? You now have to choose > > the correct inverse to get working code. I think this inconsistency is > far > > worse. > > Mathematically equivalent is first of all vague
Can I frame that quote? :P > and secondly not > relevant within most CAS since there are tons of different 0 that behave > very differently. > I agree that for a CAS, we sometimes need to sacrifice mathematical statements for programming reasons (0 is good, plus things like ==, RR). > > I agree that having x^-1 and 1/x being different is confusing. I will > update the branch at #25524 to make them identically return a rational > fraction. > I think this is even worse than the confusion. I would suspect we will get a ton of AskSage questions asking how do we construct x^-1 in the Laurent polynomial ring (maybe efficiently). At least, upon seeing this behavior, my first approach would be L(1/x) because I know I would leave the ring, but then need to come right back (well, if I didn't know that x // y was suppose to always return a result in the ring you started). > > > I think that any comparison to the integers is a bit unfair given that > ZZ > > and QQ are generally very good with ducktyping and there is no natural > way > > to create the inverse of the variables (i.e., what makes them Laurent > > polynomials) other than by division or exponentiation. > > "natural" sounds strange in that context. As already mentioned there is > > 1 // x > > to get the inverse of x. And x.inverse_of_unit() also does the job. > Nobody is going to want to type inverse_of_unit() when they want x^-1; plus I would never have thought of that to get x^-1. I had the same first thought as Jeroen with 1 // x == 0, but then I thought in terms of quo_rem, and 1 // x should return the quotient, which in this case is x^-1. However, it would take a little bit for me to realize this is what I have to do. > > Though, close to what Nils talked about, there is no straight > method for "internal division or raise error". I thought inverse_of_unit() did this? Best, Travis -- 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.
