homcubes -E -i rep3d_f.map rep3d_x.cub rep3d_a.cub rep3d_y.cub rep3d_b.cub --log v3-e.log --quiet Start time: Sun Sep 7 09:35:18 2003 HOMCUBES, ver. 3.04, 09/05/03. Copyright (C) 1997-2003 by Pawel Pilarczyk. This is free software. No warranty. Consult 'license.txt' for details. [Tech info: cube 4, qcell 8, chain 12, addr 4, coord 2, intgr 2. PBase Ok.] Reading cubes to X from 'rep3d_x.cub'... 2136 cubes read. Reading cubes to A from 'rep3d_a.cub'... 1016 cubes read. Computing X\A... 0 cubes removed from X, 2136 left. Restricting A to the neighbors of X\A... 362 cubes removed, 654 left in A. Reading cubes to Y from 'rep3d_y.cub'... 2136 cubes read. Reading cubes to B from 'rep3d_b.cub'... 2712 cubes read. Computing Y\B... 0 cubes removed from Y, 2136 left. Verifying if X\A is contained in Y... Passed. Verifying if A is contained in B... Passed. 50000 bit fields allocated (0 MB) to speed up 3-dimensional reduction. Reducing full-dim cubes from (X,A)... 180 removed, 2610 left. Restricting A to the neighbors of X\A... 0 cubes removed, 474 left in A. Reducing full-dim cubes from (X,A)... 0 removed, 2610 left. Reading the map on X\A from 'rep3d_f.map'... Done. Verifying if the image of X\A is contained in Y... Passed. Reading the map on A from 'rep3d_f.map'... Done. Verifying if the image of A is contained in B... Passed. Verifying if the image of A is disjoint from Y\B... Passed. Computing the image of the map... and of the inclusion... 3796 cubes. Restricting B to the neighbors of Y\B... 1052 cubes removed, 1660 left in A. Reducing full-dim cubes from (Y,B)... 0 removed, 3796 left. Transforming X\A into a set of cells... 2136 cells created. Transforming A into a set of cells... 474 cells created. Transforming Y\B into a set of cells... 2136 cells created. Transforming B into a set of cells... 1660 cells created. Collapsing faces in X and A... 10150 removed, 15926 left. There are 7403 faces of dimension up to 2 left in A. Note: The dimension of X decreased from 3 to 2. Creating the map F on cells in X... 157882 cubes added. Creating the map F on cells in A... 51777 cubes added. 116 bit fields for dimension 3 were used. Creating a cell map for F... Done. Note: It has been verified successfully that the map is acyclic. Creating the graph of F... 177516 cells added. Adding boundaries of cubical cells in Y and B... 21516 cubical cells added. Forgetting 4688 cells from B. Computing the image of F... 20971 cells. Collapsing Y towards F(X)... 762 cells removed, 22890 left. Creating the chain complex of the graph of F... Done. Creating the chain complex of Y... Done. Creating the chain map of the projection... Done. Creating the chain map of the inclusion... Done. Vertices used: 9053 of dim 3, 44686 of dim 6. Time used so far: 41.9 sec (0.70 min) out of 169 sec (2.8 min). Computing the homology of the graph of F over the ring of integers... Reducing D_2: 159 + 47152 reductions made. Reducing D_1: 27333 + 12307 reductions made. H_0 = 0 H_1 = Z H_2 = Z Computing the homology of Y over the ring of integers... Reducing D_3: 1766 + 37 reductions made. Reducing D_2: 2661 + 3364 reductions made. Reducing D_1: 2198 + 886 reductions made. H_0 = 0 H_1 = Z H_2 = Z The map induced in homology is as follows: Dim 0: 0 Dim 1: f (x1) = y1 Dim 2: f (x1) = y1 The map induced in homology by the inclusion: Dim 0: 0 Dim 1: i (x1) = y1 Dim 2: i (x1) = y1 The inverse of the map induced by the inclusion: Dim 0: 0 Dim 1: I (y1) = x1 Dim 2: I (y1) = x1 The composition of F and the inverse of the map induced by the inclusion: Dim 0: 0 Dim 1: F (x1) = x1 Dim 2: F (x1) = x1 Total time used: 108 sec (1.8 min) out of 321 sec (5.3 min).