2021-02-09 06:20:00 +0200 received badge ● Notable Question (source) 2017-06-06 17:12:29 +0200 received badge ● Popular Question (source) 2013-04-10 08:33:13 +0200 answered a question Matrix of vectors What I would like is to create a matrix M where M(i,j) is a vector, not just a real number! The code you gave produces a 2x2 matrix just of real numbers I believe. I want vectors to specify the entries M(i,j) of M, not the rows/columns. 2013-04-10 08:04:16 +0200 asked a question Matrix of vectors Hi. Suppose that I have a collection of vectors $v_1, \ldots, v_n \in \mathbb{R}^3$ and I wish to compute all cross products $v_i \times v_j \in \mathbb{R}^3$ where $1 \leq i < j \leq n$. Is it possible to store the output in a matrix, i.e. can I form a matrix M in Sage where $M(i,j) = v_i \times v_j$? 2012-12-01 06:55:25 +0200 received badge ● Student (source) 2012-11-30 11:41:50 +0200 answered a question Dual Cells and Face Poset Thank you! Problem solved :). I think it would be helpful to do sage: K.face_poset(options...) with options including facade=True in Sage. 2012-11-30 11:40:07 +0200 received badge ● Supporter (source) 2012-11-30 05:40:37 +0200 answered a question Dual Cells and Face Poset This is completely the correct answer! How frustrating for me! When I try to run the example (on my Macbook Pro with Sage 5.4.1 and OS X 10.8.2) sage: X = simplicial_complexes.Simplex(2) sage: find_dual_cell(X, Simplex(X.vertices()[0])) I get the error sage: Traceback (click to the left of this block for traceback)... sage: ValueError: The face ((0,), (0, 2), (0, 1, 2)) is not a subset of the vertex set. I have created a worksheet at http://www.sagenb.org/home/pub/5038 that contains all of the above code (edit: public worksheets are currently disabled) . It still produces the same error! 2012-11-29 05:55:37 +0200 answered a question Dual Cells and Face Poset Thank you for your suggestion. I only actually want to find the dual cells of vertices. I added the code "facade = True" to the existing algorithm which finds the face poset of a simplicial complex K (a warning for below- I have not done much programming before) def find_face_poset(K): from sage.combinat.posets.posets import Poset from sage.misc.flatten import flatten covers = {} all_cells = flatten([list(f) for f in K.cells().values()]) for C in all_cells: if C.dimension() >= 0: covers[tuple(C)] = [] for C in all_cells: for face in C.faces(): if face.dimension() >= 0: covers[tuple(face)].append(tuple(C)) return Poset(covers, facade = True)  I also created an algorithm to find the cofaces of a simplex $\sigma \in K$: def find_cofaces(K, sigma): m = sigma.dimension() cofaces = [] cofaces.append(sigma) for i in range(m+1, K.dimension()+1): i_faces = K.n_faces(i) for tau in i_faces: if sigma.is_face(tau): if tau.dimension() == i : cofaces.append(tau) else: pass else: pass return cofaces  and also an algorithm to find the dual cell of a vertex $\sigma$: def find_dual_cell(K, sigma): face_poset = find_face_poset(K) maximal_chains = face_poset.maximal_chains() dual_cell_vertices = find_cofaces(K, sigma) dual_cell_facets = [] for tau in maximal_chains: if sigma.tuple() == tau[0]: dual_cell_facets.append(tau) else: pass return SimplicialComplex(dual_cell_vertices, dual_cell_facets)  I played around with the example K = simplicial_complexes.Sphere(3) for sigma in K.n_faces(0): find_dual_cell(K, sigma) When I get Sage to print dual_cell_vertices and dual_cell_facets (instead of returning SimplicialComplex(dual_cell_vertices, dual_cell_facets)), it seems to produce a correct result. But it never produces the correct simplicial complex! It gives me Simplicial complex with vertex set (0, 1, 2, 3, 4) and 4 facets Any help would be very much appreciated! 2012-11-28 08:51:09 +0200 received badge ● Editor (source) 2012-11-28 08:49:45 +0200 asked a question Dual Cells and Face Poset Hello. I would like to create a procedure in Sage to find the dual cell of a simplex $\sigma$ in a simplicial complex $K$. The dual cell $D(\sigma, K)$ of $\sigma$ is a subcomplex of the first barycentric subdivision of $K$. The vertex set is given by the barycentres of all cofaces of $\sigma$, and the simplices are joins of barycentres of the form $\widehat{\sigma_0} \widehat{\sigma_1} ... \widehat{\sigma_s}$ with $\sigma \leq \sigma_0 \leq ... \leq \sigma_s$. My plan of attack is to view K as a poset, then find the maximal increasing chains $[\sigma_0,..., \sigma_s]$ in K which satisfy $\sigma_0 = \sigma$ . These chains would then be the maximal faces of the dual cell $D(\sigma, K)$. Creating the poset and finding the maximal chains of simplices is fine. However, if I have a maximal chain $[\sigma_0,..., \sigma_s]$ a problem occurs when checking if $\sigma_0 = \sigma$ - Sage sees $\sigma_0$ as just an element of the poset and not as simplex and $\sigma$ as a simplex but not an element of the poset so the equality is never satisfied. How can I correct this? Thanks, Chris .