On Sunday, December 4, 2011 7:47:13 PM UTC-8, Felix Breuer wrote: > > Hello again! > > I have followed your instructions and come up with the following: > > X = simplicial_complexes.Torus() > C = X.chain_complex(cochain=True) > print C._chomp_repr_() > H = C.homology(generators=True) > gen1 = H[1][1][0] > gen2 = H[1][1][1] > d1 = C.differential()[1] > > This works very well so far. In particular d1*gen1 gives the zero vector > as it should. Now: How can I get the bijection between the indices of the > vectors gen1 and gen2 and the corresponding 1-faces in X? C._chomp_repr_() > gives the boundary matrices in the form: > > dimension 1 > boundary a1 = - 1 * a3 - 1 * a10 > boundary a2 = - 1 * a2 - 1 * a5 > boundary a3 = + 1 * a4 + 1 * a9 > boundary a4 = + 1 * a6 + 1 * a12 > boundary a5 = + 1 * a2 + 1 * a11 > boundary a6 = - 1 * a4 - 1 * a11 > boundary a7 = + 1 * a4 + 1 * a8 > boundary a8 = + 1 * a5 + 1 * a14 > boundary a9 = - 1 * a9 + 1 * a10 > boundary a10 = + 1 * a1 + 1 * a6 > boundary a11 = - 1 * a6 - 1 * a8 > boundary a12 = + 1 * a5 + 1 * a7 > boundary a13 = + 1 * a8 + 1 * a14 > boundary a14 = + 1 * a7 + 1 * a9 ... > > > But I don't see any information what face, say, a1 corresponds to. Am I > missing something? >
You should be able to do sage: X.n_faces(1) to get the list of 1-simplices. a_i should be dual to the ith element in that list. -- John -- 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
