Sure: take x0=1/2. On Wed, 21 May 2025 at 20:20, Dima Pasechnik <dimp...@gmail.com> wrote: > > I forgot - does Sage do the Minkowski decomposition into compact and > non-compact parts (so you do have a ray in your polyhedron) > Is it even possible to define over Q a non-compact polyhedron without integer > points? > (sorry, my geometry of numbers knowledge is pretty bad) > > > > On Wed, May 21, 2025, 12:52 Vincent Delecroix <20100.delecr...@gmail.com> > wrote: >> >> Note that for triangulating, sage does not help >> >> sage: M.polyhedron().triangulate() >> Traceback (most recent call last): >> ... >> NotImplementedError: triangulation of non-compact polyhedra that are >> not cones is not supported >> >> On Wed, 21 May 2025 at 18:39, Dima Pasechnik <dimp...@gmail.com> wrote: >> > >> > PS. You also have not set an objective function, not sure, but it could be >> > why you have no termination >> > >> > On Wed, May 21, 2025, 11:37 Dima Pasechnik <dimp...@gmail.com> wrote: >> >> >> >> It should be possible to construct the polyhedron determined by the >> >> feasible set of the LP, triangulate it, and do simplex by simplex or >> >> perhaps use various results relating volumes and presence of integral >> >> points in polyhedra. >> >> >> >> On Wed, May 21, 2025, 11:27 Vincent Delecroix <20100.delecr...@gmail.com> >> >> wrote: >> >>> >> >>> Dear all, >> >>> >> >>> I have a 7 variables 3 constraints linear program that I want to solve >> >>> with integers >> >>> >> >>> x = M.new_variable(integer=True, nonnegative=True) >> >>> M.add_constraint(x[0] - x[1] + x[2] - x[3] - x[4] - 2 * x[6] == 2) >> >>> M.add_constraint(x[0] - x[1] + x[2] - 2 * x[4] - x[5] - x[6] == 2) >> >>> M.add_constraint(2 * x[0] - x[3] - x[4] - x[5] - x[6] == -1) >> >>> >> >>> However, with both >> >>> >> >>> M = MixedIntegerLinearProgram(solver="PPL") >> >>> >> >>> and >> >>> >> >>> M = MixedIntegerLinearProgram(solver="GLPK") >> >>> >> >>> The command M.solve() does not terminate in reasonable time... I do >> >>> not expect the system to have solutions, but I would like a proof of >> >>> it. >> >>> >> >>> One subtlety of the system is that there are (infinitely many) >> >>> positive integral solutions of the homogeneous version (ie linear >> >>> combination == 0). I wondered if that was the reason why it is harder >> >>> for a solver. >> >>> >> >>> If anyone knows of an alternative way to provide an open source >> >>> computer assisted proof that there is no solution I would be >> >>> interested. >> >>> >> >>> Best >> >>> Vincent >> >>> >> >>> -- >> >>> 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 view this discussion visit >> >>> https://groups.google.com/d/msgid/sage-support/CAGEwAAnr71Pi7151VHkQ0OCCYrXVhXgjc9zt5s5V3jezE%2BdUqQ%40mail.gmail.com. >> > >> > -- >> > 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 view this discussion visit >> > https://groups.google.com/d/msgid/sage-support/CAAWYfq2UvmPYJmuqHN5xRDctY2dHtOkr1k-3ymgEPw0Y1gz3Tw%40mail.gmail.com. >> >> -- >> 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 view this discussion visit >> https://groups.google.com/d/msgid/sage-support/CAGEwAAnnaXtQ8TarBkB2nd0Miw%3DsDOJUoJvW3pBpL_xc3_ENmA%40mail.gmail.com. > > -- > 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 view this discussion visit > https://groups.google.com/d/msgid/sage-support/CAAWYfq2RLtrgsBy55UHA0V6r5iZhM3Z5agmhRe9pmNjJ-h5b%3DA%40mail.gmail.com.
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