HOMCUBES, ver. 3.01, 11/29/02. Copyright (C) 1997-2002 by Pawel Pilarczyk. This is free software. No warranty. Consult 'license.txt' for details. Reading the domain of the map from 'vpol5.map'... 814 cubes read. Reading the image of the map from 'vpol5.map'... 814 cubes read. 236775 bit fields allocated (7 MB) to speed up full-dimensional reduction. Reducing full-dim cubes from X... 590 removed, 224 left. Reading the image of the map from 'vpol5.map'... 0 cubes read. Reading the map restricted to cubes in X from 'vpol5.map'... Done. Computing the image of the map... 570 cubes. Expanding B in Y... 0 cubes moved to B, 814 left in Y\B. Reducing full-dim cubes from Y... 244 cubes removed. 75 bit fields were in use. Transforming X into a set of cells... 224 cells created. Collapsing faces in X... ..... 39532 removed, 1508 left. Note: The dimension of X decreased from 5 to 1. Transforming Y into a set of cells... 570 cells created. Adding to Y boundaries of cells in Y... 77730 cells added. Creating the map F on cells in X... 9591 cubes added. Creating a cell map for F... .. Done. Creating the graph of F... . 5268 cells added. Transforming Ykeep into a set of cells... 570 cells created. Computing the image of F... 3424 cells. Collapsing Y towards F(X)... ..... 0 cells removed, 78300 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. Vertices used: 7289 of dim 5, 2634 of dim 10. Time used so far: 16.6 sec (0.28 min). Computing the homology of the graph of F over the ring of integers... Reducing D_1: 0 + 2633 reductions made. H_0 = Z H_1 = Z Computing the homology of Y over the ring of integers... Reducing D_2: 0 + 15120 reductions made. Reducing D_1: 4413 + 2626 reductions made. H_0 = Z H_1 = Z The map induced in homology is as follows: Dim 0: f (x1) = y1 Dim 1: f (x1) = y1 Total time used: 19.2 sec (0.32 min). Thank you for using this software. We appreciate your business.