On Mon, Jul 6, 2009 at 10:35 PM, Bjarke Hammersholt Roune<bjarke.ro...@gmail.com> wrote: > > I'd like to discuss whether limiting the size of exponents of > variables in Sage is a good way to go, and whether it is necessary to > report an error when breaking those limits. In the default polynomial > ring using Singular, Sage currently reports an exponent overflow error > when presented with a variable raised to an exponent larger than 2^15. > There seems to have been no discussion on sage-devel on whether this > is acceptable. Am I the only one who thinks that such a limitation is > a problem? I wonder if Magma, Maple and Mathematica have such a > limitation.
I very strongly agree that such a limitation is a major problem. The only way I can think of to deal with it, is if any such exponent appears, we switch to the polydict (nonsingular) representation, and everything gets way slower, and Groebner basis computations switch to a toy implementation + warning (or just fail with an error immediately?). However, much to my surprise the Sage-native polydict implementation is in fact broken even worse!!!! (please report this to trac). In particular, it is really sad that Sage has the following behavior too, when we're *not* using libsingular. sage: R.<x,y,z> = GF(next_prime(2^50))[] sage: type(x) <class 'sage.rings.polynomial.multi_polynomial_element.MPolynomial_polydict'> sage: x^9203482083402834 x^-1471732654 At worst an error should be raised. -- William > > There is the further issue on whether it is necessary to report an > error on overflow, which it seems is currently only done some of the > time: I tried to see if I could break Grobner bases in Sage due to > these limitations in Singular, and this resulted in these two trac > tickets, where the first is a silently wrong Grobner basis (I haven't > verified that this is indeed due to Singular): > > http://trac.sagemath.org/sage_trac/ticket/6472 > http://trac.sagemath.org/sage_trac/ticket/6473 > > Now those two examples are specifically constructed to trigger this > kind of thing, but computations of actually interesting Grobner bases > using Buchberger's Algorithm can reach high degrees even when both the > input and output have low degree. The limitations in Singular are > spelled out at > > http://www.singular.uni-kl.de/Manual/latest/sing_343.htm#SEC384 I find the above really unfortunate/sad as well. It's even worse than Magma's F4 being multimodular and breakable via some clever example. --William --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
