I was checking the new polytope commands specifically a polytope in R^2 with points (a,b,c,d,e,f) such that
e+b>= c+d e+c >= b+d a+b+c+d+e+f = 31 (this is a polytope I had worked on before so I know it very well) After several tries (documentation still sparse and incomplete) I managed to cosntruct it. Checked vertices: P.vertices() [[0, 0, 0, 0, 0, 31], [31, 0, 0, 0, 0, 0], [0, 0, 0, 31/2, 31/2, 0], [0, 0, 31/2, 0, 31/2, 0], [0, 0, 0, 0, 31, 0], [0, 31/2, 0, 0, 31/2, 0], [0, 31/2, 31/2, 0, 0, 0]] That's right, 7 vertices, the right ones (again this is a polytope I knew before) P.ambiend_dim() 6 P.dim() 6 !!!!! ====================================== The ambient dimension is indeed 6 (we're after all in R^6) but the polytope has dimension 5 for it's contained in the a+b+c+d+e+f=31 hyperplane (and thus its dimension is 1 less than ambient) Notice all vertices have coordinates adding 31, therefore it's indeed contained in the hyperplane Polymake verified this as well saying dimension is 5 Now I don't know how or where to submit a bug, but I suppose people involved with development here know so the least I can do is comment there's a bug so it's known and forwarded (and then stop doing polytope computations in sagemath for a bit longer) ======================================== By the way, on the "Polyhedron" documentation ?<tab> ieqs stands for inequalities or equalities? For the record, here's how I constructed the polytope DATA=[[0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 1], [0, 0, 1, -1, -1, 1, 0], [0, 0, -1, 1, -1, 1, 0], [-31, 1, 1, 1, 1, 1, 1], [31, 1, 1, 1, 1, 1, 1]] notice the "double" equation a+b+c+d+e+f >= 31 and a+b+c+d+e+f >= -31 (equivalent to the equality a+b+c+d+e+f=31 ) P=Polyhedron(ieqs=DATA) P.ieqs() [[0, 1, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0], [-31, 1, 1, 1, 1, 1, 1], [0, 0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0], [0, 0, 1, -1, -1, 1, 0], [0, 0, -1, 1, -1, 1, 0], [0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 1]] P.vertices() [[0, 0, 0, 0, 0, 31], [31, 0, 0, 0, 0, 0], [0, 0, 0, 31/2, 31/2, 0], [0, 0, 31/2, 0, 31/2, 0], [0, 0, 0, 0, 31, 0], [0, 31/2, 0, 0, 31/2, 0], [0, 31/2, 31/2, 0, 0, 0]] Notice that "ieqs" dropped one of the lines with 31 (so I suppose "ieqs" means equalities after all but that's incosistent with the minus sign, isn't it?) Changing DATA to use only one of those lines has no effect, same vertices, dimension still is wrongly reported as 6 --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
