CHAINMAP. Copyright (C) 1998-1999 by Marcin Mazur and Jacek Szybowski. This is free software. No warranty. Consult 'license.txt' for details. The algebraic algorithm was chosen Reading multivalued map... 100 % Completing dimension 1... Calculating domain... 100 % Completing domain... 100 % Completing dimension 0... Calculating domain... 100 % Completing domain... 100 % Writing a chain complex... 100 % Calculating dimension 0... 100 % Calculating dimension 1... 100 % Calculating dimension 2... 100 % Writing a chain map... Writing dimension 0... 100 % Writing dimension 1... 100 % Writing dimension 2... 100 % Time used: 1.35 sec (0.023 min). ------------------------------------------------------------------------ CNVCHMAP, ver. 0.06. Copyright (C) 1999-2002 by Pawel Pilarczyk. This is free software. No warranty. Consult 'license.txt' for details. Reading Cy from 'vpol2.dy'... Reading Cx and the map from 'vpol2.dat'... Completing boundaries within Cx... Writing Cx to 'vpol2.chx'... Completing boundaries within Cy where needed... * There were 1876 cells added! Writing Cy to 'vpol2.chy'... Writing the map to 'vpol2.chm'... The conversion of the chain map finished. Thank you. Time used: 0.32 sec (0.005 min). ------------------------------------------------------------------------ HOMCHAIN, ver. 2.05+. Copyright (C) 1997-2002 by Pawel Pilarczyk. This is free software. No warranty. Consult 'license.txt' for details. Reading a chain complex from 'vpol2.chx'... Reading another chain complex from 'vpol2.chy'... Reading a chain map from 'vpol2.chm'... Time used so far: 0.17 sec (0.003 min). The ring of coefficients is the ring of integers. Computing the homology of the chain complex... Reducing D_2: 785 + 29 reductions made. Reducing D_1: 714 + 409 reductions made. H_0 = Z H_1 = Z Computing the homology of the other chain complex... Reducing D_2: 780 + 34 reductions made. Reducing D_1: 624 + 499 reductions made. H_0 = Z H_1 = Z The map in homology is as follows: Dim 0: f (x1) = y1 Dim 1: f (x1) = -y1 Total time used: 0.24 sec (0.004 min). ------------------------------------------------------------------------ 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 'vpol2.map'... 814 cubes read. Reading the image of the map from 'vpol2.map'... 814 cubes read. 300 bit fields allocated (0 MB) to speed up full-dimensional reduction. Reducing full-dim cubes from X... 590 removed, 224 left. Reading the image of the map from 'vpol2.map'... 0 cubes read. Reading the map restricted to cubes in X from 'vpol2.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. 74 bit fields were in use. Transforming X into a set of cells... 224 cells created. Collapsing faces in X... .. 864 removed, 656 left. Note: The dimension of X decreased from 2 to 1. Transforming Y into a set of cells... 570 cells created. Adding to Y boundaries of cells in Y... 2330 cells added. Creating the map F on cells in X... 3774 cubes added. Creating a cell map for F... .. Done. Creating the graph of F... . 1884 cells added. Transforming Ykeep into a set of cells... 570 cells created. Computing the image of F... 1019 cells. Collapsing Y towards F(X)... .. 0 cells removed, 2900 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: 1088 of dim 2, 942 of dim 4. Time used so far: 0.27 sec (0.005 min). Computing the homology of the graph of F over the ring of integers... Reducing D_1: 0 + 941 reductions made. H_0 = Z H_1 = Z Computing the homology of Y over the ring of integers... Reducing D_2: 560 + 10 reductions made. Reducing D_1: 454 + 425 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: 0.33 sec (0.005 min). Thank you for using this software. We appreciate your business.