homcubes -i -a r2h.map --log r2h_homa.log Start time: Mon Aug 11 15:46:52 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. Reading the map on X from 'r2h.map' for careful reduction... Done. Verifying if the image of X is contained in Y... Passed. Reducing cubes from X [acyclic]... 1350807 removed, 21521 left. Reading the map on X from 'r2h.map'... Done. Computing the image of the map... and of the inclusion... 60563 cubes. Reducing full-dim cubes from Y... 1289737 removed, 82591 left. Transforming X into a set of cells... 21521 cells created. Transforming Y into a set of cells... 82591 cells created. Collapsing faces in X... 182094 removed, 162416 left. Note: The dimension of X decreased from 3 to 2. Creating the map F on cells in X... 2350057 cubes added. 50000 bit fields were used. Creating a cell map for F... Done. Note: It has been verified successfully that the map is acyclic. Creating the graph of F... 2247304 cells added. Adding boundaries of cells in Y... 826897 cells added. Computing the image of F... 352535 cells. Collapsing Y towards F(X)... 297482 cells removed, 612006 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: 1502107 of dim 3, 537902 of dim 6. Time used so far: 107199 sec (29.8 hours) out of 162948 sec (45.3 hours). Computing the homology of the graph of F over the ring of integers... Reducing D_2: 2241 + 583494 reductions made. Reducing D_1: 344451 + 193450 reductions made. H_0 = Z H_1 = Z^8 H_2 = Z^23 Computing the homology of Y over the ring of integers... Reducing D_3: 28943 + 16632 reductions made. Reducing D_2: 73429 + 77988 reductions made. Reducing D_1: 68681 + 40314 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) = y8 f (x8) = 0 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 The map induced in homology by the inclusion: Dim 0: i (x1) = y1 Dim 1: i (x1) = -y1 i (x2) = -y2 i (x3) = y3 i (x4) = -y4 i (x5) = -y5 i (x6) = -y6 i (x7) = y8 i (x8) = y7 Dim 2: i (x1) = -y10 i (x2) = y8 i (x3) = y4 i (x4) = -y16 i (x5) = -y20 i (x6) = -y5 i (x7) = -y3 i (x8) = -y21 i (x9) = y23 i (x10) = -y2 i (x11) = y7 i (x12) = y22 i (x13) = y15 i (x14) = -y12 i (x15) = -y11 i (x16) = -y19 i (x17) = y13 i (x18) = y14 i (x19) = -y6 i (x20) = y18 i (x21) = y9 i (x22) = -y17 i (x23) = -y1 The inverse of the map induced by the inclusion: Dim 0: I (y1) = x1 Dim 1: I (y1) = -x1 I (y2) = -x2 I (y3) = x3 I (y4) = -x4 I (y5) = -x5 I (y6) = -x6 I (y7) = x8 I (y8) = x7 Dim 2: I (y1) = -x23 I (y2) = -x10 I (y3) = -x7 I (y4) = x3 I (y5) = -x6 I (y6) = -x19 I (y7) = x11 I (y8) = x2 I (y9) = x21 I (y10) = -x1 I (y11) = -x15 I (y12) = -x14 I (y13) = x17 I (y14) = x18 I (y15) = x13 I (y16) = -x4 I (y17) = -x22 I (y18) = x20 I (y19) = -x16 I (y20) = -x5 I (y21) = -x8 I (y22) = x12 I (y23) = x9 The composition of F and the inverse of the map induced by the inclusion: Dim 0: F (x1) = x1 Dim 1: F (x1) = 0 F (x2) = 0 F (x3) = 0 F (x4) = 0 F (x5) = 0 F (x6) = 0 F (x7) = x7 F (x8) = 0 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 Total time used: 112940 sec (31.4 hours) out of 172240 sec (47.8 hours).