Hello! Try this sequence of commands:
sage: R = PolynomialRing(GF(32003), 'x', 4) > sage: I = sage.rings.ideal.Cyclic(R,4).homogenize() > sage: GF = I.groebner_fan() > sage: GBs = GF.reduced_groebner_bases() > sage: [g.lm() for g in GBs[0]] > >>>> [x2^2*x3^6, x2^3*x3^2, x1*x3^4, x2^2*x3^4, x1*x2*x3^2, x1*x2^2, x1^2, > x0] You would be forgiven for thinking that the leading monomials are listed there; they aren't. In fact, if you try reducing the S-polynomials of GBs[0], they won't reduce to 0. Moreover, if you try reducing the input polynomials over GBs[0], they won't always reduce to 0. sage: F = I.gens() > sage: for f in F: print f.reduce(GBs[10]) > >>>> 0 > >>>> 0 > >>>> -x1*x2^2 - x2^2*x3 + x1*x3^2 + x3^3 > >>>> -x1*x2^2*x3 + x1*x2*x3^2 + x2*x3^3 - h^4 The following indicates why: sage: TOs = GF.weight_vectors() > sage: TOs[0] > >>>> (9, 8, 3, 2, 1) sage: GBs[0][0].parent().term_order() >>>> Degree reverse lexicographic term order sage: {G[0].parent().term_order() for G in GBs} >>>> {Degree reverse lexicographic term order} In short, the Gröbner fan knows the correct ordering (in terms of a weight vector) but Sage's output presents the basis with a different ordering. This caused me no small amount of confusion. Is this a feature, or a bug? thanks john perry -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.