homcubes -EF -i rep3d_f.map rep3d_x.cub rep3d_a.cub rep3d_y.cub rep3d_b.cub --log v3-ef.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. Expanding B in Y... 1816 cubes moved to B, 320 left in Y\B. Restricting B to the neighbors of Y\B... 1052 cubes removed, 3476 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... 320 cells created. Transforming B into a set of cells... 3476 cells created. Collapsing faces in X and A... 10176 removed, 15914 left. There are 7407 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... 158612 cubes added. Creating the map F on cells in A... 51849 cubes added. 209 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... 179530 cells added. Adding boundaries of cubical cells in Y and B... 1600 cubical cells added. Forgetting 8300 cells from B. Computing the image of F... 1515 cells. Collapsing Y towards F(X)... 140 cells removed, 1780 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, 45065 of dim 6. Time used so far: 41.3 sec (0.69 min) out of 163 sec (2.7 min). Computing the homology of the graph of F over the ring of integers... Reducing D_2: 234 + 47641 reductions made. Reducing D_1: 27528 + 12532 reductions made. H_0 = 0 H_1 = Z H_2 = Z Computing the homology of Y over the ring of integers... Reducing D_3: 254 + 4 reductions made. Reducing D_2: 249 + 382 reductions made. Reducing D_1: 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: 56.4 sec (0.94 min) out of 207 sec (3.5 min).