homcubes -i r2h.map --log r2h_hom.log Start time: Sun Aug 10 14:07:58 2003 HOMCUBES, ver. 3.04, 07/05/03. 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 'r2h.map'... 1372328 cubes read. 50000 bit fields allocated (0 MB) to speed up full-dimensional reduction. Reducing full-dim cubes from X... 1350480 removed, 21848 left. Reading the map on X from 'r2h.map'... Done. Verifying if the image of X is contained in Y... Passed. Computing the image of the map... and of the inclusion... 61527 cubes. Reducing full-dim cubes from Y... 1291472 removed, 80856 left. Transforming X into a set of cells... 21848 cells created. Transforming Y into a set of cells... 80856 cells created. Collapsing faces in X... 186546 removed, 161600 left. Note: The dimension of X decreased from 3 to 2. Creating the map F on cells in X... 2320814 cubes added. 50000 bit fields were used. Creating a cell map for F... Done. *** SERIOUS PROBLEM: The map is not acyclic. THE RESULT WILL BE WRONG. *** You must verify the acyclicity of the initial map with 'chkmvmap' *** and, if successful, run this program with the '-a' switch. Creating the graph of F... 2243077 cells added. Adding boundaries of cells in Y... 796174 cells added. Computing the image of F... 353981 cells. Collapsing Y towards F(X)... 284178 cells removed, 592852 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: 1375529 of dim 3, 536853 of dim 6. Time used so far: 41628 sec (11.6 hours) out of 82909 sec (23.0 hours). Computing the homology of the graph of F over the ring of integers... Reducing D_2: 2198 + 582472 reductions made. Reducing D_1: 343465 + 193387 reductions made. H_0 = Z H_1 = Z^8 H_2 = Z^24 Computing the homology of Y over the ring of integers... Reducing D_3: 29426 + 16028 reductions made. Reducing D_2: 73992 + 72607 reductions made. Reducing D_1: 65667 + 38690 reductions made. H_0 = Z H_1 = Z^8 H_2 = Z^23 The map induced in homology is as follows: Dim 0: f (x1) = y1 Dim 1: f (x1) = 0 f (x2) = 0 f (x3) = 0 f (x4) = 0 f (x5) = 0 f (x6) = 0 f (x7) = 0 f (x8) = -y7 Dim 2: f (x1) = 0 f (x2) = 0 f (x3) = 0 f (x4) = 0 f (x5) = 0 f (x6) = 0 f (x7) = 0 f (x8) = 0 f (x9) = 0 f (x10) = 0 f (x11) = 0 f (x12) = 0 f (x13) = 0 f (x14) = 0 f (x15) = 0 f (x16) = 0 f (x17) = 0 f (x18) = 0 f (x19) = 0 f (x20) = 0 f (x21) = 0 f (x22) = 0 f (x23) = 0 f (x24) = 0 The map induced in homology by the inclusion: Dim 0: i (x1) = y1 Dim 1: i (x1) = -y1 i (x2) = y6 i (x3) = -y3 i (x4) = y5 i (x5) = y2 i (x6) = y4 i (x7) = y8 i (x8) = -y7 Dim 2: i (x1) = -y22 i (x2) = -y20 i (x3) = -y9 i (x4) = y2 i (x5) = y7 i (x6) = 0 i (x7) = -y12 i (x8) = y1 i (x9) = -y19 i (x10) = -y18 i (x11) = y17 i (x12) = -y4 i (x13) = -y5 i (x14) = y23 i (x15) = y16 i (x16) = -y6 i (x17) = -y10 i (x18) = -y15 i (x19) = y14 i (x20) = -y13 i (x21) = -y21 i (x22) = y8 i (x23) = -y3 i (x24) = y11 The inverse of the map induced by the inclusion: Oh, my goodness! This map is apparently not invertible. Total time used: 46186 sec (12.8 hours) out of 92310 sec (25.6 hours).