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 'vpol4.map'... 814 cubes read. Reading the image of the map from 'vpol4.map'... 814 cubes read. 200000 bit fields allocated (2 MB) to speed up full-dimensional reduction. Reducing full-dim cubes from X... 590 removed, 224 left. Reading the image of the map from 'vpol4.map'... 0 cubes read. Reading the map restricted to cubes in X from 'vpol4.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... .... 12432 removed, 1248 left. Note: The dimension of X decreased from 4 to 1. Transforming Y into a set of cells... 570 cells created. Adding to Y boundaries of cells in Y... 25530 cells added. Creating the map F on cells in X... 7592 cubes added. Creating a cell map for F... .. Done. Creating the graph of F... . 3920 cells added. Transforming Ykeep into a set of cells... 570 cells created. Computing the image of F... 2366 cells. Collapsing Y towards F(X)... .... 0 cells removed, 26100 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: 3753 of dim 4, 1960 of dim 8. Time used so far: 3.81 sec (0.064 min). Computing the homology of the graph of F over the ring of integers... Reducing D_1: 0 + 1959 reductions made. H_0 = Z H_1 = Z Computing the homology of Y over the ring of integers... Reducing D_2: 0 + 5800 reductions made. Reducing D_1: 2218 + 1301 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: 4.42 sec (0.074 min). Thank you for using this software. We appreciate your business.