Hi Simon, Thanks for the feedback El jueves, 19 de febrero de 2015, 18:23:27 (UTC+1), Simon King escribió: > > Hi Enrique, > > On 2015-02-19, Enrique Artal <enriqu...@gmail.com <javascript:>> wrote: > > 1. For the first one, it was already reported, with an open ticket, > but > > I am worried about it since it produces wrong outputs. > > If there is an open ticket for it, then there is no need to report it > again. However, if it gives wrong results and is not fixed soon then I > think > there should be a different ticket adding a "stopgap" (that will print a > warning to the user that the computation may have a wrong result. Has > the stopgap ticket not been opened as well? >
Not really. I do not know how to do it but I hope I will have some help tomorrow in my University > > > Maybe the point is that for Singular the actual ring defined as > > R is not the polynomial ring but the localization by the order > > That's very likely the problem. And I think that the cleanest solution > would be to take this into account by changing the string representation > of a > polynomial ring in local ordering: It should not be called > "polynomial ring over ... with generators ..." but "localisation at ... > of polynomial ring over ... with generators ...". > I agree > > (i.e., we > > can divide by any non-zero polynomial whose leading term is a > constant); in > > fact, for algorithmic purposes one always works with polynomials > (taking > > out the possible denominators wisely), but the ring is not a > polynomial. I > > guess that a small change in the way of dividing polynomial would > suffice. > > Very probably not. We would need to deviate from the polynomial backend > (i.e., Singular) fairly much to implement this, which would be > complicated and slow. > I think you are right; I think that Singular performs only polynomial computations while knowing that the actual ring is larger and this is OK for any point of view. I do not know if providing the right mathematical answer to division may force to complicate somehow the types of elements in the local rings. > > > 2. When doing some test for the above problem I realize that > *R.<x>=PolynomialRing(QQ,order='neglex') > > *does not take into account the order (the above *f* is not a unit). > > Yes, it is, since the ring is in fact localised. > > > This is not really an issue, the problem is the fact that the > function > > accept the entry *order* but it ignores it silently. > > Ahm, why do you think it is ignored? > I have rechecked that *R.<t>=PolynomialRing(QQ,order='neglex');(1+t).is_unit()* yields False > > Best regards, > Simon > > Best regards, Enrique -- 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 http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
