Hi! On 2017-11-03, 'Mark Bell' via sage-devel <sage-devel@googlegroups.com> wrote: > And so I did: >> Polyhedron(eqns=eqns, ieqs=ieqs).integral_points_count() > 1260 > > However, if I look at all of the slices obtained by fixing the first > variable x_0 (which must be 1 <= x_0 <= 100 by the first equation and > inequality) then I get the following numbers of integral points in each > slice: > >> [Polyhedron(eqns=eqns+[[-k, 1, 0,0,0,0,0,0,0,0,0,0,0]], > ieqs=ieqs).integral_points_count() for k in range(1, 101)] > [84, 84, 84, ...., 0, 0, 0] > > Which is fewer points in total: > >> sum(_) > 1197
Sorry that I am not directly answering your question. What does polymake have to say about that polyhedron? First of all, there seems to be some bug in the polymake interface (that I authored, so: Sorry...): sage: P = Polyhedron(eqns = eqns, ieqs=ieqs) sage: PP = polymake(P) The conversion of P into a polymake polytope fails first (that's the bug), but when one tries again, there is no complaint. sage: PP.VERTICES 1 1 1 46/3 1 49/3 46/3 0 49/3 49/3 49/3 0 1 1 45/2 45/2 1 1 47/2 1 0 47/2 2 2 0 1 1 45/2 1 1 1 2 1 0 47/2 2 47/2 0 45/2 1 1 1 1 45/2 2 1 0 2 47/2 47/2 0 45/2 1 1 45/2 1 45/2 47/2 1 0 2 47/2 2 0 1 sage: P.vertices_list() # Sage agrees with Polymake [[1, 1, 46/3, 1, 49/3, 46/3, 0, 49/3, 49/3, 49/3, 0, 1], [45/2, 45/2, 1, 1, 47/2, 1, 0, 47/2, 2, 2, 0, 1], [45/2, 1, 1, 1, 2, 1, 0, 47/2, 2, 47/2, 0, 45/2], [1, 1, 1, 45/2, 2, 1, 0, 2, 47/2, 47/2, 0, 45/2], [1, 45/2, 1, 45/2, 47/2, 1, 0, 2, 47/2, 2, 0, 1]] sage: PP.N_LATTICE_POINTS # Sage agrees with Polymake again. 1260 Best regards, Simon -- 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.