Sage includes cddlib, which I believe uses the Fourier-Motzkin algorithm (keeping track of both vertices and inequalities. The easiest way to access this functionality is probably the Polyhedron class, for example the following defines an unbouded region in R^3 through its inequalities (a list such as [2,0,1,1] means 2 + 0*x_0 + 1*x_1 + 1*x_2 >= 0):
sage: p = Polyhedron(ieqs = [[1, 0, 1,0], [1, 1, 0,0], [1, 1, -1,0], [0,0,0,1]]) sage: p A 3-dimensional polyhedron in QQ^3 defined as the convex hull of 2 vertices and 3 rays. You can get the vertices and rays defining this region: sage: print p.vertices() sage: print p.rays() [[-1, -1, 0], [-1, 0, 0]] [[1, 1, 0], [1, 0, 0], [0, 0, 1]] and from that you could eliminate the third variable by restricting the rays and vertices to the dimensions you want; for instance eliminating the last variable: sage: p2 = Polyhedron(vertices = [x[0:2] for x in p.vertices()], rays = [x[0:2] for x in p.rays()]) sage: p2 A 2-dimensional polyhedron in QQ^2 defined as the convex hull of 2 vertices and 2 rays. -Marshall Hampton On Jan 24, 12:47 am, tvn <nguyenthanh...@gmail.com> wrote: > hi, just wondering if the Fourier-Motzkin algorithm for eliminating > variable from a system of linear inequalities is implemented somewhere in > Sage ? -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
