homcubes -i -a rep3d_f.map rep3d_x.cub rep3d_a.cub rep3d_y.cub rep3d_b.cub --log rep3d-a.log Start time: Thu Sep 4 06:24:27 2003 HOMCUBES, ver. 3.04, 05/09/03. 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 full-dimensional reduction. Reading the map on X from 'rep3d_f.map' for careful reduction... Done. Verifying if the image of X\A is contained in Y... Passed. Verifying if the image of A is contained in B... Passed. Expanding A in X... 1491 moved to A, 645 left in X\A, 1798 added to B. Restricting A to the neighbors of X\A... 1496 cubes removed, 649 left in A. Reducing cubes from (X,A) [acyclic]... 160 removed, 1134 left. Reading the map on X\A from 'rep3d_f.map'... Done. Reading the map on A from 'rep3d_f.map'... Done. Computing the image of the map... and of the inclusion... 1978 cubes. Expanding B in Y... 22 cubes moved to B, 316 left in Y\B. Restricting B to the neighbors of Y\B... 2870 cubes removed, 1662 left in A. Reducing full-dim cubes from (Y,B)... 0 removed, 1978 left. Transforming X\A into a set of cells... 645 cells created. Transforming A into a set of cells... 489 cells created. Transforming Y\B into a set of cells... 316 cells created. Transforming B into a set of cells... 1662 cells created. Collapsing faces in X and A... 2614 removed, 5588 left. There are 7559 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... 58253 cubes added. Creating the map F on cells in A... 51204 cubes added. 236 bit fields 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... 46296 cells added. Adding boundaries of cells in Y and B... 1580 cells added. Forgetting 4636 cells from B. Computing the image of F... 1514 cells. Collapsing Y towards F(X)... 120 cells removed, 1776 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: 7715 of dim 3, 13437 of dim 6. Time used so far: 19.9 sec (0.33 min) out of 75 sec (1.2 min). Computing the homology of the graph of F over the ring of integers... Reducing D_2: 61 + 12884 reductions made. Reducing D_1: 6275 + 2111 reductions made. H_0 = 0 H_1 = Z H_2 = Z Computing the homology of Y over the ring of integers... Reducing D_3: 251 + 6 reductions made. Reducing D_2: 242 + 388 reductions made. Reducing D_1: H_0 = 0 H_1 = Z H_2 = Z Maximal homology level considered for the map is 2. 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: 21.0 sec (0.35 min) out of 79 sec (1.3 min).