On Tue, May 1, 2018 at 1:01 PM, Vincent Delecroix <20100.delecr...@gmail.com > wrote:
> On 01/05/2018 18:31, Nils Bruin wrote: > >> On Tuesday, May 1, 2018 at 9:10:27 AM UTC-7, vdelecroix wrote: >> >>> >>> Dear all, >>> >>> How should be defined division in non-integral domains like Zmod(6)? The >>> following looks a bit incoherent to me >>> >>> PPS: people with access to magma are welcome to report! >>> >>> >> Magma complains about division by a non-unit. It does allow "div", but it >> also allows 5 div 2 in ZZ/6. >> >> I think the problem for "/" is division by a zero-divisor. Otherwise an >> answer can be returned in a structure where an inverse has been adjoined. >> >> The ZeroDivisionError is therefore spot-on, if you read it as an >> abbreviation of ZeroDivisorDivisionError. Using non-unit as abbreviation >> for zero-divisor in Z/nZ is pretty common too. I don't think a change is >> necessary. >> > > But there is still something missing in Sage: how do I compute all > possible "quotients" of 5 by 2 in Zmod(6) in my Sage console other than > > sage: R = Zmod(6) > sage: a = R(5) > sage: b = R(2) > sage: [c for c in R if c*b == a] > [2, 5] > Such a function would be reasonable to implement, though note that the actual answer in your example is [], not [2, 5]. I agree with Nils that the ZeroDivisionError is correct. If there's something to be fixed, it's the divides function, which is currently using a generic implementation from element.pyx that falls back on testing whether a % b == 0. Indeed: sage: R = Zmod(6) sage: R(2).divides(R(4)) True sage: R(4).divides(R(2)) ArithmeticError: reduction modulo 4 not defined David > Vincent > > > -- > 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. > -- 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.
