homcubes --log vpol8.log vpol8.map --quiet Start time: Mon May 5 22:11:09 2003 HOMCUBES, ver. 3.04, 05/04/03. 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 the domain of the map from 'vpol8.map'... 814 cubes read. Reading the image of the map from 'vpol8.map'... 814 cubes read. 15345 bit fields allocated (12 MB) to speed up full-dimensional reduction. Reducing full-dim cubes from X... 590 removed, 224 left. Reading the map on X from 'vpol8.map'... Done. Computing the image of the map... 570 cubes. Reducing full-dim cubes from Y... 244 removed, 570 left. 75 bit fields were used. Transforming X into a set of cells... 224 cells created. Transforming Y into a set of cells... 570 cells created. Collapsing faces in X... 1104876 removed, 3204 left. Note: The dimension of X decreased from 8 to 1. Creating the map F on cells in X... 21001 cubes added. Creating a cell map for F... Done. Creating the graph of F... 11128 cells added. Adding boundaries of cells in Y... 2113530 cells added. Computing the image of F... 7628 cells. Collapsing Y towards F(X)... 2002202 cells removed, 111898 left. Note: The dimension of Y decreased from 8 to 2. 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. Vertices used: 56793 of dim 8, 5564 of dim 16. Time used so far: 4123 sec (1.1 hours) out of 4170 sec (1.2 hours). Computing the homology of the graph of F over the ring of integers... Reducing D_1: 0 + 5563 reductions made. H_0 = Z H_1 = Z Computing the homology of Y over the ring of integers... Reducing D_2: 8120 + 25929 reductions made. Reducing D_1: 14521 + 7378 reductions made. H_0 = Z H_1 = Z Maximal homology level considered for the map is 1. The map induced in homology is as follows: Dim 0: f (x1) = y1 Dim 1: f (x1) = -y1 Total time used: 4310 sec (1.2 hours) out of 4357 sec (1.2 hours).