On Fri, Apr 17, 2020 at 8:58 PM Ricardo Buring <[email protected]> wrote: > > Dear sage-devel, > > Consider the following example, sent to me by Theo de Jong (Mainz): > > sage: R.<x,y> = PolynomialRing(QQ, order='lex') > sage: I = R.ideal([x^2 + y^3 - 2*y^2, x*y^2 - 3*x*y + x, y^4 - 3*y^3 + > y^2]) > sage: f = x^2*y + x*y^2 > sage: f.reduce(I) > 3*x*y - x - y^4 + 2*y^3 > > This remainder r is incorrect, because (according to the documentation) "No > term in r is divisible by any of the leading monomials of I", while we > clearly see y^4. > The basis is a Groebner basis, and reduction with respect to the list of > polynomials gives the correct result: > > sage: I.basis_is_groebner() > True > sage: G = I.gens() > sage: f.reduce(G) > 3*x*y - x - y^3 + y^2 > > The problem seems to be that tail reduction is (unintentionally) turned off > in case the ordering is lex and reduction is done w.r.t. an ideal, as > previously reported here: https://trac.sagemath.org/ticket/27508 > As suggested by Dima Pasechnik, a workaround is to use the Singular notation > 'lp' instead of 'lex'. > Evidently, the problem lies in the communication between SageMath and > (lib)Singular. > Possible solutions (some with patches) are mentioned in the trac ticket (and > the required changes seem relatively minor), but apparently have not been > implemented yet. > Having to work around this bug in an educational setting is frustrating. Is > there a hero on sage-devel able and willing to work on a fix?
I think this is https://trac.sagemath.org/ticket/27508 which needs an effort to fix, as it's far from easy. > > Best regards, > Ricardo > > -- > 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 [email protected]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sage-devel/1ea251d3-0437-4d5c-8640-d5e0cdb628f8%40googlegroups.com. -- 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 [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAAWYfq0JckZHau-2MwFJf_Xh2uDtt_7OhpUkmZQBmk_53R3yzA%40mail.gmail.com.
