If you want to know the geometry of the solution set then you should work with cones directly:
sage: c1 = Cone([(1,0), (0,1)]) sage: c2 = Cone([(0,1), (-1,0)]) sage: c1.intersection(c2).polyhedron().Hrepresentation() (An equation (1, 0) x + 0 == 0, An inequality (0, 1) x + 0 >= 0) If you want to maximize a linear function on the solution set then you should use the MixedIntegerLinearProgram code. On Friday, November 2, 2012 10:11:04 PM UTC, Ryan Davis wrote: > > I've been trying to do calculations on polytopes, and the associated > rational polyhedral cones, cone lattice, and so on. One of the > computations I've been trying to implement computes a list of inequalities > that must hold true in terms of symbolic variables within the polytope, and > I would like to complete the complete solution set to these inequalities. > > For some of the relatively simple polytopes, the list of inequalities is > rather small, and I'm able to use solve([list of inequalities], [list of > relevant variables]) to solve for the complete solution set, which takes a > minute or two. As the complexity of the polytope ramps up, though, very > large lists of inequalities are generated, and solve() takes an immense > amount of time. > > Is there a faster way to compute the complete set of solutions to a system > of linear inequalities than solve()? From what I can see of Mixed Integer > Linear Programming, I'm not sure it computes the full solution set. I'm > not sure how I would go about expressing these inequalities in terms of > matrices, or if that's even a valid approach for a linear inequality of > several variables. Is there a different way of solving linear > inequalities, or alternatively, is my understanding of MILP incorrect? > > Thanks, > Ryan Davis > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-support?hl=en.
